A new motel chain in the U.S. is interested in the amount of time Americans spen

Question

A new motel chain in the U.S. is interested in the amount of time Americans spend in the shower. The U.S. Environmental Protection Agency reports that the average shower lasts 8.9 minutes. The distribution for these times appears to be normally distributed. If the standard deviation for these times is 3.0 minutes, find the shower length that separates the longest ten percent of showers from the remaining ninety percent of showers.

Use the Z value in the standard normal table that is closest to the required probability. Do not round any other intermediate calculations. Enter your answer as a decimal rounded to two places

Explanation / Answer

Mean is 8.9 and s is 3

P(x<X)=0.9 (we need to find a value that is at 90% from bottom)

from normal table we get z=1.28

thus z=(x-mean)/s or x=8.9+1.28*3=12.74

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