 Um, have you have you taken the assessment from the lecture on the lecture site? Would you cite? Yes, I did them last night. But it doesn't come with answers. So I got one wrong in part two and I don't know which one. Okay, no, it's fine. We will we will look at them just now and try to log into my unison. Let me just see if I can download. And others, have you done the assessments? Yes, ma'am, I've done the assessment too. I've found part two easier than part one. But like the ladies, there's no answers. So I don't really know where I went wrong. My my unison is taking longer. Mine as well. I'm struggling to even get the those blocks where you log in. No, the same thing on my side. I think I did download the exercise. The thing is with this exercises, you will notice that I might not have the same answers as you or the same questions as you have, because every student gets different exercises to do. So but we will work through the ones I have. Listen to those two. Part one and part two, yeah. So we will work through the ones I have. So we can start with part one. I also need to open the tutorial letter 101. So the other thing you need to your lecture has already sent you lots for during the past week. He has been sending new communication regarding the exam. So the last one was the guideline in terms of what procedure you need to follow in order to take the exam, where you will find your exam. And what he also wants us to relate to you guys is that I've been telling you that the exam will always be that all students will get different exam papers, even though the structure of the exam is the same. So it follows your chapters. So it first comes from study unit one until study unit 11. And we've done a trial mock-up assessments, many of them in the past. So it follows the same. So you're writing out of 25 questions is an hour. And our section. So what happens is one to open the exam paper, one to open part one. Let's say you start with section one first, one to open it. You have an hour to finish it. And then what I will suggest as well is since it is time-based. So once you start with section one, take a break after you completed, you submitted your one hour is done. Take a break of 10 minutes or so to get a breather and then come back and do section two or collect your thoughts again and then start with section two. Don't start immediately with section two after section one has finished. So the exam will be open until three o'clock. So you still have enough time. The other thing is because at the beginning when we start with the exam, everybody wants to go in. There are thousands and thousands of students who registered for 16 days. So what will happen is all of you, you will want to start the exam at the same time. You can pace yourself. You don't have to start immediately and exactly, exactly, exactly. On clock, 11 o'clock. You can give yourself time, but you need to log in on to try and see if you can log in into the system from 11 until 12 o'clock and then by 12 o'clock start with your exam. Or you can start immediately with the exam if you don't have any challenges. So don't panic because I know that the minute you start with the exam and say 11 o'clock and you start panicking when the my exam doesn't come up, the exam paper, you can see all those things. Don't panic. You will eventually write because the exam is extended until 3 o'clock in that afternoon. So you still have ample time to take any of the two sections, but make sure that you pace yourself. And our online is not easy. So start with section with cut one first. Make sure that you complete that because also when you are writing the exam, you don't have the, I'm not sure on the assessment does it allow you to go back. So you won't be going back. So you need to make sure that whatever you answer at that point, you are sure that that is the correct answer that you have. When it comes to sections where you will require the tables, I will suggest that you also immediately before you even start with your exam, open up your tutorial letter 101, scroll to the back of your exam paper until you get to the tables and leave it open at from that point where the tables start. Because when you start writing the exam, especially when you go to section two, which will start with study unit six, when you get there, you need to make sure that your tables are open because it's that with normal distribution, you will require, oh, sorry, from section one, when you get to the discrete probabilities, when you start with the binomial and Poisson, you need to have the tables open so that you don't waste time going to find resources. Also, the other thing is make sure that you have your cheat sheet formula. I'm going to call it a cheat sheet formula bank next to you already with chapters relating to every, like you have chapters and formulas that relates to those sections. Because this is just an open book, even though you should treat it as an exam, and you must use the opportunities that are given to you as well because some exams, they were procted, so it means you cannot use additional material to support you to write the exam. But now you can use that because they are available. But if you feel you don't want to use that, then you want to see how much you know about stuff, you don't have to have that cheat sheet next to you with formulas. That will help you write the exam better. Because anyway, if you were going to sit in the exam in a venue, you were going to be given the formulas and the tables to use. So it still works out the best for you to at least have all the formulas because in the exam they don't give you all the formulas as well. So use those opportunities as well. And lastly, yeah, lastly is take a breather. Don't leave your phone, don't look at it, don't do anything, make sure that treat on doing your exam because the chances are, the more distracted you are with the phone, the time will be running. It moves fast, it moves quickly. So leave your phone somewhere or switch it off and turn it down. Remove all the distractions that might happen while you're taking the exam. And that's the only thing I have for you. And then we can start. I wanted to also open the, sorry, I haven't opened it yet. Let me share my screen. Okay, so this was also, and this is part one. And you can go through them one by one. But before I do that, I need to also open the tutorial letter one on one, which has tables. So those who haven't taken the online assessment, I will urge you to practice. It's not about getting the answers right or wrong. They are there to help you see the structure of your exam and make you feel comfortable when you start writing the exam. I know the practice sessions are two hours long hair section. So you can also time yourself. So you can do it the first time and see how long it takes you and do the second time and see how long it takes you to answer only one part. And the practice assessment, they had 11 questions, 11 questions, which were 22 questions overall, which will not be the case. In the normal exam, you are writing out of 25 questions. So it might be 12 questions for the first section and 18th section for the next section, or it might be 14th section for the I don't know how it looks. I don't know how your exam looks. But all I know is the structure of your exam follows your study unit. So this is tutorial letter one on one. I just want to scroll to the table so that when we start using tables, I know that I have them ready there. We can start with section one. I'm going to assume because we only have two hours. I'm going to assume we can extend it with additional 30 minutes so we can finish at half past four. I don't have any hurry today. And I assume that everybody who's here has at least tried this assessment. And because you also directly receive, let's say what you call that answers. I'm not sure if they did they tell you that question one is incorrect or correct? Did you find those or not? You only get your scores that says you got 22 or you got 44 or something like that. You only find your scores. Yes, you only, sorry. You only find your scores. They don't give you the answers. Oh, I see. I see. Okay, so there's no need. I can just give you all the answers for all the questions. You can also go back and look at your questions as well because remember, like I said, every student would have received some sort of a different question at some point. But there will be those questions that are common that everybody will receive. And then there will be those questions that everybody, some people might not receive it in that way. So for example, I think this one is one of those common one, everybody should have received this kind of a question. I am not sure. I don't know how your exam looked like. So also remember that the structure also I can also take you through the structure quickly. So you will remember that the structure for questions will always be two questions per chapter or one question. Yes, two questions per chapter because you're writing out of 25. So it will be two questions per chapter. And for some instances with exceptions, there will be three questions per chapter. So you must always remember that because if you know what chapter you're dealing with, you will know what questions and what to look out for. So we can start with question number one and then we can quickly and quickly. And I'm assuming or I cannot assume because you don't have your, your assessments with you. So we can look at question. Let's do it this way. We look at question by question. But I'm scared that we might not finish because two hours if we go through every question by question, we might not get it right. So if we look at the first question that was asked, it asked which one is and they give you the statement about the COVID-19 and then they asked you. So because this is chapter one, we know chapter one we deal with what the statistics, what are the types of variables, what are the levels of measurement, but it's a population, what is a sample statistics and what are the branches of statistics. You need to know all those things. So if you read through this question, you can see that it talks about types of variables. And we know that we have two types of variables and we have four types of levels of measurement. And we know that the two variables quantitative, quantitative. One is numerical. So quantitative is numerical. And when it's numerical, it can be counted or it can be observed. And when it's counted is continuous. And when it is measured, sorry, when it's measured, it's continuous and when it's counted is discrete. And we also know that we have a categorical variable which has the categories. And out of those, we can then find the levels of measurements. Remember the four levels of measurements, nominal, ordinal, interval and ratio. Nominal and ordinal are for categorical variable. Ratio and interval are for numerical are for the numerical variable. And we know that nominal variables, nominal variables are, are variables that you can put into categories, but there is no order. So means and no rank to them. And we also know that we have the, we have ordinal variables which are variables that can be placed in order or they've got rank. Then we have also, we have what we call interval and, interval and ratio. And we know both of them are, they come from numerical variables where with, where with interval variables, we know that they, they, there is no zero and with the ratio, there is two meaning of zero. So looking at that, not going to go into too much detail. The first question was asking is the number A, is this a qualitative nominal variable? Number two is asking is this a quantitative discrete variable? Is this a qualitative nominal variable? Is this a continuous variable? And this is a qualitative nominal variable. So which one would you, which one is incorrect? The symptoms, if they are in this categories, since they are already placed in categories, we know that those are qualitative variables. Is there rank or order in those variables? No. There is no rank in that variable. So therefore it means they should be a nominal variable. So this is correct. So, but we're looking for the incorrect one. Then we'll move to the next statement. The next statement says yeah, we're talking about the number. Is the number qualitative or quantitative? No, the answer, oh, oh, you know what? On my side, I've got the exact same question, but it said which one of the following statements is correct. Yes. Remember, that's what I said. Sorry. I thought I said you are going to receive different questions. It's a second question. The last one says correct. Oh, wow. Yes. Someone is correct. So now based on the one that we have right now in front of us, but surely we have, we're going to go through this one. So, but you will have, I remember now, wait, sorry, let me also take that. Remember here, I'm giving you the skill on identifying which question, it got less of the question that you are given. How will you know which weather, which answer you need to choose? Is by interrogating every statement. And yeah, I'm giving you a hint on how to save time as well in interrogating those statements. So you can see that I'm not reading the whole statement. So I'm highlighting I'm highlighting only key, key issues here that will guide me in terms of answering the question. So the first thing is to look at what the question is saying. Look at what kind of answers I need to be getting from each statement and then start interrogating what you have in that, because the minute you see the options that you have, it tells you what kind of question is that. Then when you start looking at the key things from the question, you can link the key issues to the statements and find the correct answer. So number two is asking the number, is the number qualitative or quantitative and these are the things that you're going to ask yourself in your mind. Because it's a number, it means it's a qualitative variable. And since it is number, so therefore it's going to be counted. And when it's counted, we say it is discrete. Okay, so we know that number A and B are correct. Now we're looking for number C. C says name, we know that it's a qualitative nominal. So let's look at this. So it has named our list of provinces. Is this qualitative or quantitative? It's qualitative. It's qualitative. So it means this is correct. And name our list of provinces. Is it in order? Is there a rank or no rank? And if there is a rank, it's ordinal. And if there's no rank, it's nominal. Is this a nominal or ordinal? It's a nominal. It's nominal. So this is also correct. Then we move to the next question. Medical cost of each patient in rent. In rent. Is this qualitative or quantitative? It's quantitative. Remember, guys, I'm not only talking to one person. I am talking to everybody at this point. Everybody should have their mics unmuted if they don't have any noise, but you are all allowed to talk. It is quantitative. And is this continuous or discrete? Now, here is the catch. Okay. Because of this extension in rent, if it was only cost, if they just said a cost of each patient, that would have been, this one I'm giving it to you because I need to explain this. If they only mentioned the cost of each patient, the question would have been a continuous variable or not. Because, yeah, okay, I'm going to change it back. Because of the cost and the cost is in rent, in this statement, usually if they, for example, sometimes I'm going to say this, it's not always the case. Sometimes a continuous variable can be converted to a discrete variable, to a counted variable, but not in this instance. So in this instance, you can just ignore the rent because also with the rent, it's still, the money will still always, money is always in decimal. Even though it says to rent, it will still be dot zero zero. It will still be a continuous variable, but there are measures sometimes where they will tell you that this is a continuous, and they will add other things. For example, if they say days, how many years or age, let's take age, for example, age. Age is always going to be a continuous variable because we always count, so we're always going to measure it in terms of days, seconds, minutes, and all that. But if they say days in years, remember now, when it's in years, you cannot measure them again. You can count them because years can be counted. But when it comes to prices, you, prices will always remain in a decimal point, even though it's always going to, even though you write it to the nearest rent, but there's always going to be a decimal for cents, and those cents will be equivalent to zero zero. And that is why this question will be continuous. You need to be very careful when you answer questions. You need to also interrogate that. Is it, can it convert from a continuous to a discrete variable? So this is continuous variable. I just wanted to make sure that you understand that concept, those concepts. Numbers E, they ask, they're giving the severity, and they give you a small, moderate, and severe, and yet they're giving you the highest, the lowest, and the middle. So is this a qualitative or quantitative? And it is in order, so it should be ordinary. And that's how you will answer the questions in the exact. So moving on to the next question, the next question they gave you, any question before we move to the next question. The next question, it means I'm going to make it smaller. The next question. I have the same, I have the same question on my side. Yes. And it's asking for the incorrect. Some people might get the one that says which one of this is correct. And you might also, you will get the same table. So all of you will get the same table. Yeah. The only thing that might be different, the other thing that might be different will be the incorrect or correct. And the statements might be correct. So you might get a different statement to this. Yes. Okay. So yeah, they're asking which one is the incorrect one. So you said the reason why I said you must stay away from the WhatsApp and all that is because you're going to get confused because people on WhatsApp will start giving each other answers. But it might not be the right answer for your question that you receive in your exam. You will get this, you are writing the same exam, but the options might be different. And the questioning might also be different. So be very, very careful because they try to avoid what happened in semester one where everybody was sharing answers. So yeah, they made it, they made sure that you need to be sure that you're getting your own individual questions and there are no copying or plagiarism happening on the exam paper, on the exam. So here they give you a frequency table and they're asking you statements. The first thing they're asking you is percentage of Dumalanga. So you don't have to go ahead and create a presentation for all of them and end. You're only going to answer, concentrate on what statement they have given you. So yeah, they're asking you percentage for Dumalanga. So you're going to take Dumalanga and you're going to divide by that thing. What answer do you get? 4.5, 4.6, 0.46. So that is correct. Then they're asking you what is the relative frequency. So wait, whoa, wait. Percentage remember is that divided by that multiplied by 100. So you will say 71 divided by 15, 5, 1, 5 multiplied by 100. That is the percentage. A relative frequency is the same thing. So if they would have asked for a relative frequency, you would have just done 21 divided by that. It will be in decimal. So relative frequency is a decimal point. So yeah, we need to calculate relative frequency for Eastern Cape. So you go to Eastern Cape and divide Eastern Cape by 15,500. Do you get the same answer? So this should be the answer you see in front of you will be the answer for relative frequency for Eastern Cape. 0.12. And that's the relative frequency. And then you go to see they're asking the frequency of Northwest. So frequency is the actual number that they would have given you. So what is the frequency of Northwest? You go to Northwest and you get the frequency and it says it's 70. Is it correct? That is not correct. Once you get your answer that you are looking for, you move forward. Don't say I need to make sure that all the statements are correct. No, we have our answer. Then we can move forward. Then we move forward to the next question. And our next question, which is three. And yeah, I'm sorry. I want to show you all the answers. Okay. Here they give you what is this? Who can tell me what are we looking at here? And this is question number two and question number three from chapter three. What is this? Yeah, but what they call this? They give you the stem and leaf plot and they will ask you question relating to chapter three and chapter two. So this is chapter and unit two in terms of the stem and leaf plot. But if you look at the question, they're asking you things from chapter three or study unit three, which is measures of central tendencies and measures of central location and all that. So now based on this information that you have, remember how to read the stem and leaf, the number they in front is one. The second one is 43 and so forth. You need to repeat in that way. So that when you do the calculations, you calculate it right. So the first question they ask you is, oh, we need to look for the incorrect question. And remember, once you get the answer, you need to make sure that you move to the next question. So they're asking you questions about the shape of the distribution. So this is the shape. You need to always remember that for a normal distribution, it looks like a belly shape calf. For a left skewed, I don't know how to draw. It will look like this. And for the right skewed, it will look like that. So this we call it asymmetric. This we call it left skewed or negatively skewed. Or negatively skewed. And this we say it is right skewed or positively skewed. So if you look at these three graphs and you look at this information, is this symmetric or normally distributed? It's not symmetric. It is not symmetric. So therefore, we're looking for the incorrect one. And therefore, this is the incorrect one that we're looking for. Let's say your question was asking you for the correct one. So you will continue and look for the correct one. So you need to be sure how to calculate the mean. The mean is the sum of all of them. So you will add the 1 plus 43 plus 63 plus 70 plus 80 plus 89 plus 96 and divide by how many they are? One, two, three, four, five, six, seven. That should give you the mean. The mode is the number that appears more than the other numbers. Not the number that appears not the highest number. So is this question, does it have a number that appears more than the others? No, there is not. So therefore, you can check the answer by looking at the table. The range, remember the range? So if I write here, the mean is the sum of all of them divide by n. The range will be your highest value minus the lowest value. So you will take 96 and subtract a 1. That will give you your range. And then the median is the middle of it. Remember the middle value? We can find the position by saying n plus 1 divided by 2 will give us the position of the median. We were on three, we go to four. So four also is a stem and leaf block. Yeah, they're asking you the measures of variation. They're asking you about the quartile, interquartiles and all that. Remember the quartiles? n plus 1 divided by 4. Position, these are the positions. Physicians, quartile 2, n plus 1 divided by 2 to find the second position. The quartile position 2. The third one is the third factor, which is 3 times n plus 1 divided by 4. Use this to find the position and go find the quartiles. The data is already ordered from lowest to highest. You can just use this to count them. Then the other thing, remember, if it's 0.25, we round it off. We round it down. If it's 0.75, or if it's 0.75, let me not say 0. If it's 0.75, we round it up. And if it's 0.5, if any of this position takes up any of this number, the values like this, then we take the average of the two values. So we start by calculating the quartile 1. They are 7. If I recount 1, 2, 3, 4, 5, 6, 7, they are 7. So quartile 1 will be n 1 plus n plus 1 divided by 4. It will be 7 plus 1 divided by 4. And they are looking for the position. So is that the answer? Is it correct? It's correct. Yes. That will be 8 divided by 4, which is 2. Interquartile range. So when they ask for interquartile range, or that's the other thing that I didn't say, they need the value of quartile 3 minus the value of quartile 2. Since we're looking at value of quartile 1 and value of quartile 3. So question E, D, and C, they're asking you those questions. So I think we can go to question C and see if C is correct. So C is asking first quarter. We've calculated the quartile position. So we go and find the quartile value. So your quartile value is on position 2. So it's 1, 2. It's 43. 43. So this is correct. So already we have 43. And we need to go find position for third quarter. Third quarter is 3 times n plus 1 divided by 4. 3 times 8 divided by 4 because I'm just taking 7 plus 1. And this is calculation. Where are we? That should be 6. Is it 6? So that is the position. Now we go count. 1, 2, 3, 4, 5, 6 is 89. Is that 89? Oh, so that is correct. So the value of third quartile is 89. Because you that 1, 2, 3, 4, 5, 6. And when we read it we also in 8 and 9. So that is the correct one. Therefore you can just substitute 89 minus 43. Is it the cost of all? 46. 46. So therefore it means me is the incorrect one. So you will see that some of the questions in the exam will take you longer. Some of them will take you short time. So you will need to look at the questions in totality in so that we don't waste a lot of your time as well. Okay. Okay. So the next question. Before we move to the next question, any question? Anybody? Are you lost? Are you here? Because we have so many people online but I only talk to three or four people. Just wanted to clear me here. Yes. When it comes to inter quartile range, which figure must we use? Must we use the first figure on the first quarter, on the third quarter, and then use the last figure on the first quarter? Nope. You use the value. So what do you mean the first one on the first quarter and the last one? No. The first value on the third quarter and then the last value on the first quarter. To get the inter quartile range. You use the actual values like the last remember. Okay. Let me put it this way. Remember this is a stem and leaf plot. We can write this as 31 for 363. You can unpack it so that it looks like this. Seven zero eight zero eight nine and nine six one two three four five six seven. You can write it out like this. The first patch which is the position by using this gives you the position. It gives you the chance to go and count where must you be to find the actual value of your quarter. For example, this one's on position two. So we know that this is quarter one because one two is the position, but the actual value of the quarter is 43, which is the quarter one. So if we go to the third one, which is the third quarter, we also go and find the position which is on position six. It's just to help us count the value. One, two, three, four, five, six, where it stops and we'll say this is our quarter. Three. We take the value that locates that we find on position six. Okay. That is why I don't understand your question by saying which one do we take the first one or the second one? No, I wonder. When you count these numbers, because this is in order from highest to lowest, this is one, two, three, four, five, six. So we count one, two, three, four, five, six. That will be six, but we know that we don't take only nine. We also need to include the state, which is eight. Okay. I'm clear now. Okay. This is also a stem and leaf, and here they're asking you to calculate the coefficient of variation. Now, remember your calculator. So here is where you can also save time by using your statement calculator. You can do that because calculating the standard deviation, because this is, let's look at this, this is a sample. So we can use the sample standard deviation. So calculating the sample standard deviation, which is the sum of your observation minus the mean squared divided by n minus one, it will take you forever to calculate because your coefficient of variation is equals to your sample standard deviation divided by your sample mean multiplied by a hundred. Remember that is the formula. So to calculate this, it might take you longer, and to calculate the mean, it might take you longer. So what you will do is you go to your calculator and do the state mode. Different calculators, we did this. Go look at the steps that we used when we did this chapter three, when we did the calculator. Somebody's mic is doing an echo. So I am going to use my calculator and give you the answers, but you will need to go and use your calculator to do the measures of central location. Those who are using the calculator, you go say second function mode, and so you go and do your mode, and you press one for your state one, and you press zero for state zero, and your calculator will say state zero. Then you start capturing your data. You will use the m plus. This is those who are using the sharp scientific calculator or the sharp business financial calculator. On the business financial calculator, you will use an E and T. Those who are using the sharp financial, the sharp scientific calculator, you will use the m plus. You will start by saying the two one m plus or E and T, and it will say data set one, and you go 43 E and T or m plus, and it will say data set two, and you continue to capture all the values until you've captured all of them, and it will say data set eight. Sorry, data set seven. And then when you have that, you press the on and off your calculator, and you are ready to calculate your standard deviation. Remember your standard deviation and your mean are written in green, and they are on button number four and button number five. This is those who are using the sharp scientific calculator or the sharp business financial calculator. So you press alpha and you press the five button and say divide by alpha, and you will press the button number four and press equal, and it will give you the answer and multiply your answer by 100 and say equal, it will give you your answer. For now, I'm going to do things manually. Alpha five equals is 23 so that everybody has the values, especially those who don't know how to use their calculator, and they're going to calculate manually. It will be three point seven, six, seven. Remember you need to keep all the decimal, my financial calculator, I kept it at four decimals, and you need to find your alpha four, which is my mean, which is 67 point four to 86. So you can use all the values on your calculator. And for this, I'm going to just do the answer 23 divided by 67 multiplied by 100, and I get the five. Remember, those who are using, and this will be a person. Those who are using a sharp calculator. Remember, instead, also going to take you through your steps. Those who are using a cashier, sorry, a cashier, you also need to put your calculator to state mode. Open my other calculator. I'm able to open it right now. So remember to put your calculator to state mode, and it will say SD as well. So you will say mode, STA, you will find your functions. I think it will be on button number one, zero button number one. I'm not sure. Depending on the kind of calculator you have, and you will press that SD for the standard deviation, and your calculator will give you a table with an X value. So remember to capture your values, you will say, to capture your values, you will say that you are equal, and it will place it into the table. And for 63 equal until you capture all the values up until line number seven. Once you have all the values on line number seven, you go and you say shift because your values are hidden on button number one under the STAT on button number one. And those who are using another old version of cashier, it will be under the SVAR on button number two. So either you're using the one way it has the STAT, or you use the one that has SPAM and SVAR on button number one. You will use the SVAR. Those who are placing button number one, you also follow the steps, but you will see all the steps. All the steps, you just press the values that corresponds to all those, and then there will be VAR and you choose that one. And that VAR will give you your values for standard deviation, the mean, and all that. And you will select the number that corresponds to it, and you will substitute into the formula and calculate. And for this, that's how you can see. So I'm not going to take you through all the steps because my calculator now doesn't want to open. Thank you. And those who are calculating manually, so that will be the standard deviation and the sum and the mean you will calculate using the sum of your observation minus one. So it means you calculate first the mean. I find in the mean which will be 67.43, you will say that one minus 67.43 squared plus 43 minus 67.42 or 43 squared plus 63 minus, until you get to 96 minus 67.43 squared divided by 8, sorry, seven minus one. And you calculate that, take the square root and it will give you, the outside will give you 3.768. So that will be the standard deviation. So you can use your calculator to save time instead of calculating manually. Okay, so question six is relating to this contingency table and we're looking for the incorrect question. And this will be done in question six and question seven, so you can move forward. What they did do is give you the total. Now, if you look at this contingency table, in class, we dealt with events, which are numerical value and we calculated the probabilities. Here they give you the probabilities. As soon as you see decimals, you must know that these values in here are probabilities. These are already probabilities calculated. What they didn't calculate is your marginal probabilities. So this we call them the joint probabilities. So they calculated the joint probabilities. You need to find the marginal probabilities or what we call the symbol probabilities. You cannot get away with this. So you need to just make sure that you quickly calculate those probabilities and finish it up. So this here is 0.38 plus 0.15 and it will give you 0.530 for that. And continue and do the same thing on the other side, 0.18 plus 0.29 and 0.47. And anyone has calculated the site? It's 0.056 and 0.44. And once your contingency table is complete, you can answer any probability questions that you have. So since here they give you statements, not in terms of formulas, but the nice thing about it is at the end, they also give you the probability function that you need to also be aware of. So this question, I don't even have to read what the statement says. I can just go to that that is. So it says I need to find the probability of home and secure. This is a joint probability. Is that correct? We're looking for the correct answer. Remember that. Is that correct? That is incorrect because the probability of home and secure is 0.38. So that is incorrect. Number two is asking the probability secure given that home. So since this is a conditional probability, remember you would have written on the equation somewhere close by which would have said probability of A given B is given by the probability of A and B divided by the probability of B. You would have written this somewhere on a piece of paper somewhere and you can just reference it. Take the same question that you have here, which says the probability of secure and home. You can rewrite it in terms of that. So if I see that secure is A and H is B, so I can say this is the same as the probability of secure and home divided by the probability of home. The way would I find the probability of secure and home, we calculate, we found it, it was 0.38. Divide by the probability of home. I go to home and I look for simple probability because at this point it's my simple probability of home, which is 0.23. And to calculate this, what do you get? 0.716. 0.716. It's 0.712. 717. So which is 0.712, which is correct. So you can stop right here, yes, because it's rounded, yeah, we need to round it to 2 decibels. So you can stop right here or you can continue and answer all this. So this is the probability of home, which is what we just used. And this is calculating the probability of home or secure. So depending on what kind of a question you receive in the exam, remember this might not be the one that you receive. So to find the probability of home, you will say this is the probability of home or secure is given by the probability of home plus the probability of secure minus the probability of secure and home, which you would have used the probability of A or B, which is the probability of A plus the probability of B minus the probability of A and B. That is the same equation that I used there, and you can check that. For home or secure, you can also do the same thing as what we did with secure and home. So that will be the final probability. Our answer for this session will have been option number B, because we're looking for the correct answer. Depending on the one that is there in front of you, you will know which one will be the correct one. So I'll urge you to go and do, if you haven't done your assessment online, go and do your assessment because the answers you will get or the questions you will get will not be the same as the one that you just did. Okay, so remember that first question relates to this one. And now I need to go get all the answers that I needed for this. So do you still remember what do we have here? What's 0 comma? 0, 5, 3, and 4, 7. 0, 5, 3, and 0, 4, 7. And here we had 5, 6, and 4, 4. 0.5, 6, and 0.4. So same here there. Now here they're asking me to know if you know. So they need to know if you do understand what independent means, what mutual exclusive means, and what a compliment event means. So starting with mutual exclusive, remember mutual exclusive, events cannot happen at the same time. So it means the probability of A and B will be equals to 0. This is for mutually exclusive event. For independent events, it means the probability of A given B will be the same as probability of A because students they have no bearing on each other. Or the probability of B given A will be equals to the probability of A. Or it will be the probability A and B will be given by the probability of A and the probability of B. Remember that. And a compliment event will be the probability of A will be 1 minus the probability, or the probability of a compliment will be the probability of 1 minus the probability of A. Or the probability of A is 1 minus the probability of a compliment. So based on those four statements that we have there. So this is independent and this is compliment. So based on those statements that we did there, let's come and answer these questions. Is the probability of home insecure or insecure, home and insecure, are they independent? So based on this information, I can use this information and check if they are independent, if they are independent, then they are not independent. If they are not the same, so it means the probability of home and insecure, which is 0.15, 0.15 needs to be the same as the probability of home times the probability of secure. They need to be the same. And if they are the same, then we will say they are independent. So if the statement holds, they are dependent. So what is the probability of home and probability of secure, probability of home is 0.53 multiplied by the probability of insecure, not S, the probability of insecure, which is 0.44, 0.44. If you compare this, what do you get? 0.43 multiplied by 0.44 is 0.2332. Therefore, they are not. So these are not dependent. Not independent. So this is correct. We're looking for the incorrect one. Number two, it says the probability of home and away are mutually exclusive. So it means this should say home and away equals to 0. Are they equals to 0? Home and away, home, away. They are equals to 0 because they cannot happen at the same time. So therefore, this is the correct answer. This is correct because they cannot happen at the same time. They will be equals to 0 because home and away, they are in the same category. Now we move to the next one, which says home and secure are independent. And secure, are they independent? We just didn't say. We did insecure. We can also do the home and secure. So you do the same. So we know the probability of home and secure. So you say the probability of home and secure should be equals to the probability of home times the probability of secure. So what is the values for home and secure? Home and secure is 0.838. Oh, sorry, 0.38. The probability of home is 0.53. The probability of secure multiplied by 0.56. Are they the same or not the same? So you will say 0.53 multiplied by 0.56 equals 0.30. 0.30. 0.30. So they are not independent. And this question says they are independent. So this will have been the question that we are looking for because it's asking for which one of these statements are incorrect. So it should have said not independent. And you can look at the probability of secure. Probability of secure and insecure. Probability of secure and insecure will be equals to 0. And the compliment, oh, sorry, they say it's not the probability, but the event. Event secure and insecure, they will be compliment events. So that will have been the correct one because there are a compliment of each other. Okay, moving to the next one. So here we're talking about probability, but what are we talking about here? So here we are in the binomial distribution probability. So this is the binomial distribution. So to save time, yes, to save time, never try to use the formulas because you will take forever to answer all these questions using formulas. Use the table. So if you go to the binomial distribution table, remember the table looks like this. The hint is to read the statement and find out what your N is. And here our N is 20. Our N is 20. So if the N is 20, it means we're going to be going to look for the table that has N equals to 20, which will be the last table in the binomial distribution. We just rotate it, rotate it. And there is the binomial distribution table. Remember the following as well. The values at the top, we read them with the values on the left. The values at the bottom, we read them with the values on the right, always. So these two, they go together. You read, if the probability is, it takes up any of these values, we use the ends from the right. If the probability of success is any of those values, we use the ends and the excess from the left. We go back to our question. Our probability of success, which is our pi, is 0.35. So we know that we're going to look for our pi of 0.35. That will be our table that we're going to be using. So it means our N will be using the one on the left. Going back to the question, they are asking for the incorrect question. So the key hint here is the statements, the statements are important. Those are very important. So the first one, it says the probability that all 20 branches, so it means we're looking for the probability of X is equal to 20. That's what we're looking for for number A. For number B, we're just going to write them all here. The probability that exactly 14, so we're looking for the probability that X is equal to 14. And number B, at most, 14. So it means C. We're looking for the probability that X is less than or equal to 14. The island of space, I'm going to write at the top as well. The last one, last two, at least 14 and none of 20. So D, it says the probability of X greater than or equal to 14. And E says the probability that X is equal to zero, because it says none of them. So it's equals to zero. So we know that our probability is zero comma 35. Our N is 20. We are on this. So to find the first one, it says the probability that X is equals to 20. It means we go to N 20, X 20, and for 20 for the answer. So they should be zero. It should be not applicable. So if we go back to our question, actually we should have stopped right there because it says the probability that X is equals to 20 is 0.35. Therefore, the incorrect answer would have been that one. Since we're doing all of them, so we can go and do all of them and then come and check the answers from here if they are correct. So that will be how you will do it on your exam as well. So the probability of X is exactly 14. It's equals to 14. So we go to 14. And as you can see, I cannot, you will be waking online. You will not be able to read all these values like this. So you can start counting them until 14, starting at zero. This will be zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, eighteen, fourteen. Zero comma one. Zero comma zero, one, two. That will be the probability of equals to 14. The probability of X less than or equals to 14, it means I must add all these values. Therefore, I can also say it's one minus the probability that X is greater than 14, which means I must just add only those two values that I have, which is the probability of one minus the probability of zero. I cannot do that. One minus the probability of X is equals to 15, which is 0.0003 plus the probability that X is 16, which is zero comma zero, zero, zero. This is one minus zero comma zero, zero, three, which is zero comma nine, nine, nine, seven. That is the probability of less than. Otherwise, if you have time, you can add all of them. You don't have the national to do that. So take shortcuts. The probability of X greater than 14, which will be greater than 14, it means including from here going down. So it means we go and say zero comma zero, zero, one, two, plus zero comma zero, zero, zero, three, plus zero comma zero, zero, zero, zero, which is zero comma zero, zero, one, five. The probability that X is equals to zero will be zero comma zero, zero, zero, two, because it will be just that one probability there. And that's how we will answer the question in the exam. But remember, if they are looking for the incorrect one, and you find the incorrect one, you don't have to go through all the steps. I'm just showing you on the table how you can find all these probabilities. As you can see, we find all of them, which was not easy, but we found all of those probabilities is another question. But this, remember, you get one question per section. So this is a poison distribution. So if you read the question, you will notice that it has some hints as well that tells you what you're looking at. So this is a poison, and it says good traffic describes the number of customers entering a location of instance, upon moving to level four of the national lockdown, food traffic at the mall was estimated to be 20 customers per minute. They used what we call estimation, so that will be your lambda is equals to 20 per minute. As soon as the traffic follows a poison, what will be the probability that, so yeah, we find the probability X is equals to, what will be the probability that take five customers at a given point and pass the probability that X is equals to 25. What will be the variance, which is our lambda? What is your lambda? What is the probability that eight most 35 customers will enter? What will be the probability that X less than or equals to 25 will enter? What is the mean? The mean is your expected value. We're looking for the incorrect answer. So we can automatically from using the two questions that we can eliminate that are correct. We know that the average is 20, so this is correct. We know that variance is lambda, which is correct. So we need to calculate the probabilities. So we need to go to the poison table, rotate, and yeah, on the poison, let's hope they gave us up until 20 because they gave us the average of 20. And there we go, our lambda 20. That's what we found on the estimate is 20. What will be the probability of 19? These are also 20, so all of them are lambda 20. So we just need to find the one that says 19, X is 19, 19, 0.088. That will be our probability of 19, which is that, which is correct. Now we need to find the probability that it's equals to 25. So you go find 35, where is 35? It's 0,007. 0,007. We're looking for the incorrect one automatically because all the statements are correct. I can just come here and say this is the incorrect one. Or you can go and calculate it by, because we're looking for the probability that X, sorry. So to save you time in the exam, probability that X is less than 35, so is the probability that X is less than 35 will be given by one minus the probabilities that X is greater than 0. So it's greater than 35. So it means you're going to add all this and subtract them from one. So this is 6, 7, 8. 1 minus 0.008. And if you calculate that, because if I add all of this, they will give me 0,008. 1 minus 0.008. 0.992. Which is not the correct one. So but in the exam, you will save more time because you don't have to go and do all these calculations to validate your answer. Because if all these other statements are incorrect, then it means that one will be correct. That will be the incorrect one, but also based on your assessment that you will get, you need to make sure that you do the right one. So I will still edge you. Those who haven't done this online, go and try and see if you can answer those questions online, because your questions might not be the same as what we just did right now. Okay, next question, which is the second last one I think. It talks to the sampling distribution. Sorry, normal distribution. This is a normal distribution question. They give you the mean, they give you the standard deviation. They ask you to find the probability, so therefore it means you need to go find the probability that exists. So it would be greater than or equal to 2460. So now, going back to the normal distribution, remember, we will use the table. The probability of z less than 8 is the value we find on the table. So this will be the table they do. The probability of z greater than 8, so say 1 minus the value we find on the table. The probability of between, it will be the probability of z less than b minus the probability of z less than 8, which will mean the value we find on the table for b minus the value we find on the table for a. So this is at least, so at least means greater than, so we are going to say 1 minus the value we find on the table. 1 minus the probability of z less than the x minus the mean divided by the standard deviation, which is the formula for our z distribution. So 1 minus the probability of z less than our x is what is given in the question, which is 2460 minus our mean is always going to be given in the statement, which is 3730 divided by our standard deviation of 1000. 1 minus the probability of z less than 8, and let me know what you find. Minus 3 minus 1300. Remember this, we're going to the z table. So it's minus 1 comma 3, so we need to take this minus 1 comma 3 and go to the z table. You will go to the z table and go to the negative side of the table. And on the negative side of the table, we're going to look for minus 1 and 3 on the side and 0 at the top. So that is 0 at the top and minus 1 comma 3, that will be the answer. 0 comma 0, 9, 6, 8. And you can hear you say 1 minus 0 comma 0, 9, 6, 8. I hope I 9, 6, 8. And you say 1 minus 0. 0, 9, 6, 8 equals and that will give you your answer unless somebody gave me the wrong answer for minus 1.3. It must be 1.27. 1.27. Yeah, it was minus 1.27. Do not round off quickly. Remember when you do the normal distribution table, you're always going to use two decimals. So we need to go back. So the answer was not that, it was 1.27 minus 1.27. So we come here, we look for minus 1.201234567. And that will be the answer, which is 0.1020. So yeah, 0.1020. And the answer is 0.8980. So some of you might have the question here saying at most some of you might get the one that says equal, some of you might, not equal. So some of you might get the one that says between. So you need to know how to apply when you get the values on the table. And that's why I did that way. And this is also a normal distribution question. It's a suppose your value of your X or Z value, if I go find the probability, we find it as 0.04. Remember also the probability of Z less than a value A. So if our value A is Z in this instance, please say it is the table value. So if we know that that is the table value, therefore it means the table value contains 0.4000. So can we go and find the probability of Z and find that value that it should be? So to do that, we go to the table. So for this one, you just come here to the table. We're going to look for the Z value. So we come here, we look for 0.4. So go, this is 0.00, go down and look for 0.4. So yeah, 0.4, 0.4, 0.4, 1, and then go to 0.3, 0.7, and 0.40. So it is 1, 2, 3, 0.2, minus 0.2, so at least at most equal to 0.2. It's minus 0 comma, we can always do it that way. 0 comma 2, we can use this one and go up, up, up. It's 0 comma, 0 comma 2, 5, 0 comma 2, 2, 5, minus, minus, 0 comma 2, 5. So let's look, minus 0 comma 2, and then this one, they say minus 0 comma 2, 5, 2, 5, 5.