One of the most important pieces of information you can derive about your business processes is how often a given event tends to occur. Arrival times are described by the exponential probability distribution.
- [Instructor] One of the most important pieces of information you can derive about your business is how often a given event tends to occur. For example, if you sell products via your company's website, knowing the average time between orders helps you plan the number of employees you'll have on duty at the time. Arrival times are described by the exponential probability distribution. I'll demonstrate how to use it in this movie. My sample file is the Exponential workbook. You can find it in the Chapter Four folder of your Exercise Files collection.
You need to know three pieces of information to calculate a probability using the exponential distribution. The average time that something occurs, the time you want to check, and whether you want the probability of that specific time, or the probability that a task will be completed, or perhaps an order will arrive in a given time or less. I have my workbook set up so that I can look at customer orders that occur on an average of every 50 seconds. So I have seconds from one to 150 in column A, and then in column B I have probability calculations, but right now I just have zeros entered into those cells.
If I want to calculate the probability that an order will occur exactly one second after the previous order, I can use the values in cell A2 and E1 to calculate that. So I'll click in cell B2, type an equal sign, and the function they use is expon.dist so that is E-X-P-O and then I'll pick the top of the two highlighted functions. They are actually the same but Excel updated the naming of a lot of statistical functions with Excel 2010, so I prefer to use the new name expon.dist.
So I'll press tab. Now I need to know my X and that is the number of seconds that's in cell A2, and I'll leave that reference relative so when I copy the formula, it will change, then a comma, lambda is one over the average, so one divided by and then the average is in cell E1. So I'll click cell E1 to add it. I don't want this reference changing, I always want to refer to that cell, so I'll press F4 to make it an absolute reference, and then I'll type a comma, and now I need to select whether I want the cumulative probability distribution, and that is this value or less, or the probability density function, which is the probability of exactly one second occurring.
I'll start out by doing the probability density function, so I will highlight false and press tab, type right parentheses and Enter. I see that the probability of the next order coming in at one second is about .19, just under .2, so that's about 2%. I can copy my formula from B2 to the rest of the cells that have seconds values in column A. So I click cell B2 and then move the mouse pointer over the bottom right corner, which is where the fill handle is, and when my mouse pointer changes to a black crosshair, I'll double click, and I see the values in my worksheet and also in the chart.
Let's go over and take a look at the chart. You can see that it is increasingly unlikely that an order will occur at a specific time as that time gets later. It appears that a lot of orders, relatively a lot, will occur after about one second, and then you have a slow decline past the average, and then getting down towards zero as you approach 150 seconds. Now let's take a look at the opposite case where we're looking at the cumulative probability function, in other words a specific time or less.
I'll double click cell B2, and I will change the last argument, which is false, indicating probability density function, so I'll double click that and I'll enter true so now we're looking at the cumulative probability, press Enter, and there's my value. I will click cell B2, double click the fill handle, and there you see the cumulative probability. We start at one second with a low probability, and we go up approaching one as we reach 150 seconds.
As you can see, it is very likely that most orders will take about say 35 seconds or so, because that's where the curve appears across the 0.5 or the 50% probability line. If you want to find the probability that an order will occur between two times, say between 10 and 15 seconds, then all you need to do is to subtract the smaller value from the larger. That means that I will put in the value for 15 seconds, and subtract the cumulative probability for 10 seconds.
So in cell E3, I'll type an equal sign and I'll just click the cells where those calculations occur. I will click cell B16, which is the value for 15 seconds, and I will subtract the value in cell B11. The percent of orders that will occur between 10 and 15 seconds inclusive is 7.79%.
- Distinguish between the mean, median, and mode.
- Describe the relationship between variance and standard deviation.
- Identify a nondirectional hypothesis.
- Point out the difference between COVARIANCE.P and COVARIANCE.S.
- Explain correlation.
- Analyze Bayes’ rule.