Question

engineers want to design passenger seats in commercial aircraft so that they are wide enough to fit 95 percent of adult men. assume that adult men have hip breadths that are normally distributed with a mean of 14.4 inches and a standard deviation of 1.1 inches. find the 95th percentile of the hip breadth of adult men.

Answer 1

the 95th percentile of the hip breadth of adult men when mean is 14.4 and deviation 1.1 is 16.49

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean  and standard deviation , the zscore of a measure X is given by:

Z= X- u/σ

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

u=14.4 and σ=1.1

Find Upper P 95

This is X when Z has a pvalue of 0.95 So it is X when Z = 2.327.

Z= X-u/σ

2.327 *1.1 = X - 14.4

X= 16.49

Upper P 95= 16.49 in.

learn more about of mean here

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