The maintenance staff of a large office building regularly replaces fluorescent ceiling lights that have gone out. During a visit to a typical floor, the staff may have to replace several lights. The...

The maintenance staff of a large office building regularly replaces fluorescent ceiling lights that have gone out. During a visit to a typical floor, the staff may have to replace several lights. The manager of this staff has given the following probabilities to the number of lights (identified by the random variable
) that need to be replaced on a floor:

(a) How many lights should the manager expect to replace on a floor?

(b) What is the standard deviation of the number of lights on a floor that are replaced?

(c) If a crew takes six lights to a floor, how many should it expect to have left after replacing those that are out?

(d) If a crew takes six lights to a floor, find the standard deviation of the number of lights that remain after replacing those that are out on a floor.

(e) If it takes 10 minutes to replace each light, how long should the manager expect the crew to take when replacing the lights on a floor?