• Suppose that the longevity of a light bulb is exponential with a mean lifetime ofsevenyears.

(a) Find the probability that a light bulb lasts less than one year. (Round your answer to four decimal places.)

(b) Find the probability that a light bulb lasts betweensixandeightyears. (Round your answer to four decimal places.)

(c)Sixtypercent of all light bulbs last at least how long? (Round your answer to two decimal places.)

(d) A company decides to offer a warranty to give refunds to light bulbs whose lifetime is among the lowesttwopercent of all bulbs. To the nearest month, what should be the cutoff lifetime for the warranty to take place? (Round your answer up to the next month.)

(e) If a light bulb has lastedsixyears, what is the probability that it fails within theseventhyear. (Round your answer to four decimal places.)

• A web site experiences traffic during normal working hours at a rate oftwelvevisits per hour. Assume that the duration between visits has the exponential distribution.

(a) Find the probability that the duration between two successive visits to the web site is more thanelevenminutes. (Round your answer to four decimal places.)

(b) The top 25% of durations between visits are at least how long? (Round your answer to two decimal places.)

(c) Suppose that 20 minutes have passed since the last visit to the web site. What is the probability that the next visit will occur within the next5 minutes?(Round your answer to four decimal places.)

(d) Find the probability that less than8visits occur within a one-hour period. (Round your answer to four decimal places.)

• At an urgent care facility, patients arrive at an average rate of one patient everynineminutes. Assume that the duration between arrivals is exponentially distributed. (Round your answers to four decimal places.)

part (a)Find the probability that the time between two successive visits to the urgent care facility is less thanfiveminutes.

Part (b)

Find the probability that the time between two successive visits to the urgent care facility is more than19minutes.

Part (c)

If 10 minutes have passed since the last arrival, what is the probability that the next person will arrive within the nextnineminutes?

Part (d)

Find the probability that more thansevenpatients arrive during a half-hour period.