Question

Support requests arrive at a software company at the rate of 1 every 20 minutes. Assume that the requests arrive as events in a Poisson process.

1)What is the probability that the number of requests in an hour is between 3 and 5 inclusive?

2)What is the probability that the number of requests in a 10 hour work day is between 34 and 38 inclusive?

3) What is the standard deviation of the number of requests in a 10 hour work day?

Answer 1

The average number of requests per hour is;
\[\frac{60}{20}\times 1=3=\lambda\]
\[P(X=3)=\frac{e ^{-\lambda}\lambda ^{3}}{3!}=you\ can\ calculate\]

Answer 2

You use the Poisson distribution formula:
\[P(X=x)=\frac{e ^{-\lambda}\lambda ^{x}}{x!}\]
to calculate P(X=3), P(X=4) and P(X=5). Then you add the 3 results to find the answer to 1).