EXAMPLE 5.16 Number of Wi-Fi Interruptions

Suppose that the number of wi-fi interruptions on your home network varies, with an average of 0.9 interruption per day. If we assume that the Poisson setting is reasonable for this situation, we can model the daily count of interruptions using the Poisson distribution with . What is the probability of having no more than two interruptions tomorrow?

We can calculate either using software or the Poisson probability formula. Using the probability formula:

Using Excel, we can use the “POISSON.DIST()” function to find the individual probabilities. The function has three arguments. The first argument is the value of , the second argument is the mean value , and the third argument is the value “0,” which tells Excel to report an individual probability. For example, we put the entry of “= POISSON.DIST(2, 0.9, 0)” to obtain . Here is a summary of the calculations using Excel:

The reported value of 0.93714 was obtained by using Excel’s SUM function. Excel’s answer and the preceding hand-computed answer differ slightly due to roundoff error in the hand calculation. There is roughly a 94% chance that you will have no more than two wi-fi interruptions tomorrow.