 Statistics and Excel. Exponential distribution in seconds. Roller coaster line example. Got data? Let's get stuck into it with statistics and Excel. You're not required to but if you have access to OneNote we're in the icon left hand side. OneNote presentation 1576. Exponential distribution in seconds. Roller coaster line example tab. We're also uploading transcripts to OneNote so you can go into the view tab. Use the immersive reader tool. Change the language if you so choose. Be able to either read or listen to the transcript in multiple different languages using the time stamps to tie in to the video presentations. OneNote desktop version here in prior presentations. We've been thinking about how we can represent different data sets both numerically using calculations such as the average or mean, the quartiles, the median and pictorially using the box and whiskers and histogram. The histogram being the primary tool we visualize when thinking about the spread of data and we can describe the spread of data on a histogram using terms such as it's skewed to the left, it's skewed to the right. We're now looking at functions or formulas that have a smooth curve or a line related to them which oftentimes can approximate actual data sets in the real world and if we can approximate our data sets with a line that would be great because it'll typically give us more predictive power over whatever it is we're looking into. In prior presentations we looked at families of these types of formulas, these curves including the uniform distribution, the Poisson distribution, the binomial distribution. Now we're looking at exponential distribution. Now the exponential distribution often has a relationship to the Poisson distribution so oftentimes we're going to kind of flip the question around when thinking about a Poisson distribution to the question that we'll be thinking about with an exponential distribution. So oftentimes with a Poisson distribution just to set the groundwork we're talking about in business scenarios line waiting situations where we ask questions such as what's the likelihood that so many people will be arriving within some interval of time like one minute or one second. For example we also had a problem not over time but over distance such as how many pot holes would show up in a mile of road but we're going to now look at our time example. So if we think first about like the Poisson and then we'll kind of convert that to the exponential for a line waiting situation for like a roller coaster ride for example x is going to be the arrivals during one minute and we're going to say that the mean is going to be 3.25 so the 3.25 is the mean arrivals within the time frame distance of one minute. So this is going to be the Poisson distribution not the exponential this is just the starting point. If I was to graph this out x is going to be equal to the arrivals during one minute so what's the likelihood that zero people arrive in one minute we're going to say that that's going to be the 3.88 according to our Poisson dot dist function which is going to be taking the x which is going to be this is we have a range here a spill that we're taking that's why the hashtag is there comma the mean 3.25 and then the cumulative it's not cumulative that's why it's going to be a zero because we're looking at just the zero we did that all the way down what's the likelihood that one person shows up in the one minute time frame the 12.6 what's the likelihood that two people show up the 12.48 if I wanted to know the likelihood of having zero to three people show up within the one minute time I can then say 3.88 plus 12.6 plus 20.48 and so on so we looked at that in a similar presentation in our prior practice problems and we can also look at the the curve would look something like this so here's our our Poisson curve so now we're going to say okay well now we want to ask a different question and say the minutes between arrivals so now we're getting to our exponential distribution so now we're saying all right well if there's going to be a mean of 3.25 people arriving within a one minute time period what's the what's going to be the mean minutes between arrivals so you see how we kind of flipped it on its head we're looking at the minutes between arrivals well that means we can take the the the 3.25 divided by what hold on other way around one divided by one minute divided by the 3.25 and that gives us about our