Answer to Question #323846 in Statistics and Probability for Bless

Question

 After your complaint about their service, a representative of an insurance company promised to call you “between 7 and 9 this evening.” Assume that this means that the time T of the call is uniformly distributed in the specified interval.

(a) Compute the probability that the call arrives between 8:00 and 8:20.

(b) At 8:30, the call still hasn’t arrived. What is the probability that it arrives in the next 10 minutes?

(c) Assume that you know in advance that the call will last exactly 1 hour. From 9 to 9:30, there is a game show on TV that you wanted to watch. Let M be the amount of time of the show that you miss because of the call. Compute the expected value of M.