 Hi, this is Dr. Don and I want to go over a problem from the homework. This has to do with using the binomial probability table to find probabilities for various values of x and a number of binomial distributions or binomial random variables. I want to encourage you not to use the tables in this course. You can do it, but it's time consuming and I find people tend to make more errors when they use the table than if they use technology, particularly stat crunch for solving binomial random variable problems is extremely easy to use and fast. So let me show you here, we'll breeze through these six questions. I'm going to click on question help, open up stat crunch, takes a couple of seconds here to open and I'm going to move this over here so we can see. The first problem says for x equal 4, find the probability of x equal 4 for binomial distribution within a binomial random variable with n equal 10 for the sample and the probability distribution of 0.3. Remember that that's all we need to use a calculator or to go into the tables is to know the sample size and also their probability. So I'm going to go into stat calculators binomial and we bring up our basic dialog box for the binomial calculator and we're on the standard side right here and I want to put in my value of n which is 10 is the same but my p is 0.3 and the first question x equal 4 so I click on that box to set the operator to be equal. I want 4, click on compute and we get a probability of exactly 4 that's why I added the red bar there on the histogram of 0.200 and that's the answer they need there. The next one B, remember to change that this time n is equal to 15 and p is equal to 0.6 and we need probability of less than or equal to 5. Click on compute and we've got our distribution again we can see that we've got those discrete values of x less than or equal to 5 is 0.034 and that is the answer they have there. The next one C is with an n of 5 and a p of 0.5 so I put n equal 5, p is equal to 0.5 and I need greater than 1 so I'm going to click greater than 1 to compute and there's our distribution we've got greater than 1 would be a 2, a 3, or 4, or 5 and the probability is 0.8125 which rounds to 0.813 which is the answer they have. The fourth problem is with an n of 15 and a p of 0.8 and this time it's for x less than 6 so I get the less than operator I put in 6, click compute and I've got a value there of 0.000 which rounds to 0.000 and that's the answer they have here. The next one is an n of 20 I hope you're getting this pattern down 0.6 for the p value we need greater than equal to 6 so I've clicked that operator and greater than equal to 6 this distribution there you can see we get 6 over here and we all we have to 20 is 0.998 which is the answer they have and the final one is an also an n of 20 but a p of 0.2 and it's x equal to 4 and click compute and we get 0.218 which is the answer they have there just so you'll know that those were all simple tests just for a single value of x but if you have a question where you're asked for let's say what is the probability between two values here if I leave the at the end at 20 the probability of 0.2 and it just offered up the probability of x being between 3 and 6 is 0.7 if I change this to 12 and 0.4 and 3 and 11 compute whoops what did I do there oh it's got to be 0.4 it helps have the decimal in there so you can make typos 0.4 now the probability of p being from 3 to 11 is 0.912 or 917 so you can use the between calculator if you're asked for a between problem so learn to use stat crunch it's very very quick remember all you had to do for binomial or any of these calculators is click on stat calculators there's the binomial there's the normal that we use a ton we'll later on get the t distribution the f distribution the chi square distribution and we can make a custom one I think I showed you that in another video how we can create our own custom calculator to make these problems go faster so don't be intimidated by stat crunch it's very very friendly and almost everything you do either start with data or stat and 95% of them start with stat so jump in hope this helps