6.43 In deciding how many customer service representatives to hire and in planning their schedules, it is important for a firm marketing electronic typewriters to study repair times for the machines.

Such a study revealed that repair times have approximately an exponential distribution with a mean of 22 minutes.

a Find the probability that a repair time will last less than 10 minutes.

b The charge for typewriter repairs is $50 for each half hour or part thereof. What is the probability that a repair job will result in a charge of $100?

c In planning schedules, how much time should be allowed for each repair so that the chance of any one repair time exceeding this allowed time is only 0.10?