The velocity of a car follows the distribution given by

(1) What is  ?

(2) If the distance between cities A and B is 165 mile, what is the probability that the travel time from city A to city B is less than 3 hours?

Solution

(1) Let the velocity be . Since

(2) The velocity should be greater than  mile/hr if the travel time between cities A to city B is less than 3 hours. Then the probability that the travel time from city A to city B is less than 3 hours is calculated by