• The speed of cars passing through the intersection of Blossom Hill Road and the Almaden Expressway varies from11to 35 mph and is uniformly distributed. None of the cars travel over 35 mph through the intersection. find the probability. "P(18<X<58) = ___"(Enter your answer as a fraction.)
• Suppose that the length of long distance phone calls, measured in minutes, is known to have an exponential distribution with the average length of a call equal to8minutes.

(a)Find the probability that a phone call lasts less than10minutes. (Round your answer to four decimal places.)

(b)Find the probability that a phone call lasts more than10minutes. (Round your answer to four decimal places.

(c)Find the probability that a phone call lasts between6and10minutes. (Round your answer to four decimal places.)

• Suppose that the useful life of a particular car battery, measured in months, decays with parameter0.02. We are interested in the life of the battery.

(a)Find the probability that a car battery lasts more than38months. (Round your answer to four decimal places.

(b)70%of the batteries last at least how long? (Round your answer to two decimal places.)

• The time (in years)afterreaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about6years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement.

(a) Find the probability that the person retired after age71. (Round your answer to four decimal places.)

(b)In a room of 1,000 people over age80, how many do you expect will NOT have retired yet? (Round your answer to the nearest whole number.)

• The cost of all maintenance for a car during its first year is approximately exponentially distributed with a mean of$200.

(a)Find the probability that a car required over$340for maintenance during its first year. (Round your answer to four decimal places.)