 Statistics and Excel. Exponential distribution. Create and compare sample line weighting data to exponential distribution. Get ready. Taking a deep breath. Holding it in for 10 seconds. Looking forward to a smooth soothing Excel. Here we are in Excel. If you don't have access to this workbook, that's okay because we'll basically build this from a blank worksheet. But if you do have access, there's three tabs down below. Example. Practice blank. Example, in essence, answer key. Practice tab. Having pre-formatted cells so you can get to the heart of the practice problem. The blank tab. Blank worksheet so we can practice formatting the cells within Excel as we work through the practice problem. Let's go to the example tab to get an idea of what we will be doing. Looking at an exponential distribution situation within business scenarios that often deals with line weighting situations as we will be working here. Oftentimes it's related to a Poisson distribution that we've seen in prior presentations. Poisson distributions typically asking a question such as what's the likelihood for a certain number of customers to be arriving within a certain time interval, such as minutes or seconds, whereas the exponential distribution kind of flips the question a bit and is asking what's the interval of time that is going to be passing before between customers. So what we would like to do this time is try to simulate a situation where we're going out there and we're just basically have our stopwatch and we're marking down the time that is passing between consecutive customers and if it's following up an exponential distribution then we'll be able to plot it out and possibly recognize that and compare that then to the smooth exponential distribution curve to try to get a better intuitive understanding of what is actually happening here. Alright let's go to the blank tab and start this out. We're going to say that first we'll say that the mean well let's format the worksheet. Don't get ahead of yourself. Format the worksheet. We'll hit the triangle up top right click on the worksheet and format the entire worksheet. Currency negative numbers bracketed and red no dollar sign. We'll get rid of the decimals for now. Add them as we need them. Okay I'm going to embolden the entire sheet home tab font group emboldened. I have been emboldened to proceed. Alright here we go. No fear now because we've been emboldened. So we have the mean arrival rate and this is going to be in hours. So the mean arrival rate meaning the average arrival rate we're going to imagine is 10 meaning we're imagining that on average 10 people arrive on hour. Now again when we're thinking about the number of people that arrive in a time interval that may follow a Poisson distribution and if it does then we would think that the intervals between arrivals would typically be following the exponential distribution. Alright so then we could say that the mean arrival rate in minutes then if that if it's 10 in an hour the mean arrival in minutes is going to be equal to 10 divided by 60. I'm going to add some decimals so we're going to say home tab number group adding some decimals so we have about 0.166 people arriving per minute now. Okay so then and so obviously we have to be thinking about what kind of time interval which would be best used for whatever we're working with hours, minutes, seconds and so we can say then the inter arrival time in hours so the the inter arrival time between how long does it take between arrivals would be equal to 1 divided by 10. So if we think about in hours how long does it take for people to be showing up we're going to say home tab font group add some decimals 0.1 hours right so it's probably easier to see this in minutes so if I say the inter arrival time in minutes we're going to say well how many people show up 0.166 I'm sorry one let's say one minute divided by the average people that arrive in a minute 0.1666 and we'll say enter so that comes out to about exactly six I think home tab number adding some decimals exactly six okay so so now that we have let's try to see if we can simulate this data as though we're we're out there with our stopwatch and trying to and trying to see how many people are showing up and how long it takes between each person showing up so I'm going to make a skinny see here I'm going to say that the customer and we'll try to count the number of customers that come in right so let's say let's just say we do this for like 300 customers let's say so I'm going to say then we have one two I'm going to select those two and copy it down to 300 it's going to say copy it down to 300 and we're just watching these customers come in to pick up our data I just made up 300 as a random number so I'm going down to 300 you could use the sequence fill to fill that in if you so choose and then we have the let's call it the inter inter arrival times I'm going to make this a header format selecting these two go into the home tab alignment wrapping the text centering it make it black and white okay so now we're going to use a formula now to simulate this this data it's a little bit of a complex formula I can't just use a random generator and we don't have the same kind of a random generator we saw with the poisson distribution and the binome with the data analysis so I'm going to I'm going to try to make my little random generator here imagining that we're sitting there and we're simulating us checking out how many people are showing up in the interval of time between people showing up right we're just collecting our data so that's going to be equal to uh uh ln which is going to be the natural logarithm so we have to so don't we're not going to be using a lot of calculus here but we need that for our random generation and then I'm going to say one minus the random now we're going to enter our random generation number embedded and then we're going to say close that up and I'm going to divide that by then the uh which one is it it's going to be the mean arrival rate let's do it in minutes here and then I want this b2 to not move when I copy it down so I'm going to select