Support requests arrive at a software company at the rate of 1 every 40 minutes. Assume that the requests arrive as events in a Poisson process.

a. What is the expected number of requests in an hour? Give an exact answer. ANS: 1.5

b. What is the probability that the number of requests in an hour is between 3 and 5 inclusive? Give your answer to four decimal places.

c. What is the expected number of requests in a 10 hour work day? Give an exact answer.

d. What is the probability that the number of requests in a 10 hour work day is between 38 and 42 inclusive? Give your answer to four decimal places.

e. What is the standard deviation of the number of requests in a 10 hour work day? Give your answer to four decimal places.