1. A postal letter carrier has a route consisting of five segments with the time in minutes to complete each segment being normally distributed, with means and variances as shown:

Tennyson Place N(38, 16)

Windsor Parkway N(99, 29)

Knob Hill Apartments N(85, 25)

Evergreen Drive N(73, 20)

Chastain Shopping Center N(52,12)

In addition to the times just mentioned, the letter carrier must organize the mail at the central office, which activity requires a time that is distributed by N(90,25). The drive to the starting point of the route requires a time that is distributed N(10,4). The return from the route requires a time that is distributed N(15,4). The letter carrier then performs administrative tasks with a time that is distributed N(30,9).

(a) What is the expected length of the letter carrier's work day?

(b) Overtime occurs after eight hours of work on a given day. What is the probability that the letter carrier works overtime on any given day?

(c) What is the probability that the letter carrier works overtime on two or more days in a six-day week?

(d) What is the probability that the route will be completed within 24 minutes of eight hours on any given day?