Overtime occurs after eight hours of work on a given day., Ask an Expert

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A postal letter carrier has a route consisting of five segments with the time in minutes to complete each segment being normally distributed with mean and variance 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 above times, the letter carrier must organize the mail at the central office, which 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).

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? What is the probability that the route will be completed within +/-24 minutes of eight hours on any given day?

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