SOLUTION: Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 50 minutes and a standard deviation of 10 minutes. Let X be a rand

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Question 973095: Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 50 minutes and a standard deviation of 10 minutes. Let X be a randomly selected finishing time. Find the 95 percentile point.
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Answer by reviewermath(1029) About Me  (Show Source):
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Assume that the finishing times in a New York City 10-kilometer road race are normally distributed with a mean of 50 minutes and a standard deviation of 10 minutes. Let X be a randomly selected finishing time. Find the 95 percentile point.
Solution:
P(Z < 1.645) ≈ 0.95
We want to find the 95th percentile x such that
%28x-%28mu%29%29%2F%28sigma%29 = 1.645
%28x-50%29%2F10 = 1.645
x = 10*(1.645) + 50 = 66.45
Therefore, the 95th percentile point is highlight%2866.45%29 minutes [2 decimal places]