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Exam1Sp2011_key

# Exam1Sp2011_key - NAME KEY Stat 205 Exam I There are four...

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NAME: KEY Stat 205 Exam I There are four problems total. Each lettered part of a problem is worth 6 points; there are 120 points total. However, your exam grade is out of 100 points, so there are 20 points of possible extra credit for this exam. Write clearly and show steps for partial credit. This exam is open book. 1. The time to completion of the Rome marathon in 1996 is approximately normal with mean μ = 230 minutes and standard deviation σ = 36 minutes. Let Y be the time from a randomly selected runner at this race. (a) What is the probability of a randomly selected runner completing the race in under three hours, Pr { Y < 180 } ? Answer : Pr { Y < 180 } = Pr Y - 230 36 < 180 - 230 36 = Pr { Z < - 1 . 39 } = 0 . 0823 . (b) What is the probability of a randomly selected runner completing the race within three to four hours, Pr { 180 < Y < 240 } ? Answer : Pr { 180 < Y < 240 } = Pr 180 - 230 36 < Y - 230 36 < 240 - 230 36 = Pr {- 1 . 39 < Z < 0 . 28 } = Pr { Z < 0 . 28 } - Pr { Z < - 1 . 39 } = 0 . 6103 - 0 . 0823 = 0 . 528 (c) What is the probability of a randomly selected runner completing the race with a time over five hours?

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Exam1Sp2011_key - NAME KEY Stat 205 Exam I There are four...

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