Response to the following problem:
Ernest D. Johnson is a discount stock brokerage firm located in Sun Valley, Idaho. Johnson is the only employee, and he works out of his house, where he receives all customer orders by telephone. Johnson receives an average of 10 client calls per hour, and he spends an average of 4 minutes speaking to each client. If a client calls while Johnson is talking to another client, the caller is placed on hold. The call-waiting system Johnson has leased from the telephone company allows him to keep an unlimited number of callers on hold, and he believes that no customer placed on hold will hang up before talking to him. If customer calls arrive according to a Poisson distribution and the time required to provide service to a customer follows an exponential distribution, determine:
a. The probability that Johnson will receive exactly 4 calls in a half hour.
b. The probability that Johnson will receive 3 or fewer calls in a half hour.
c. The probability that a telephone conversation will last less than 3 minutes (from the time Johnson begins speaking with the client).
d. The average number of callers waiting on hold.
e. The average time a caller will spend on the phone when calling Johnson.
f. The percentage of time Johnson is on the phone.
g. The probability that a customer will spend more than six minutes on the phone when calling Johnson.