(Please answer part a and part e)

A large service depot has a clientele of large companies with extensive computer equipment. The average number of service calls they receive every day over an 8-hour period is 3. They employ three highly trained technicians and other supporting staff. Every service call requires one technician for the entirety of the day on which they are called.

(a) Define the random variable.

(b) What is the probability that on a given day (i.e., 8 hours long), there will be exactly 4 service calls?

(c) What is the probability that there will be more than three calls in one day (i.e., 8 hours long) so that the three technicians will not be sufficient?

(d) One day, there were no service calls in the morning and one technician was allowed to take the afternoon off. In the remaining four hours of the afternoon, what is the probability that there will be more than two service calls in the afternoon so that the service depot will not be able to meet the full service needs with only two technicians?

(e) Verify the calculation of the probabilities calculated in steps (a), (b), and (c) using EXCEL function POISSON.DIST. Do you get the same result? The function POISSON.DIST can be invoked following the same steps of BINOM.DIST.