Question

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 95​%of all males.​ (Accommodating 100% of males would require very wide seats that would be much too​ expensive.) Men have hip breadths that are normally distributed with a mean of 14.4  in. and a standard deviation of 1.1in. Find Upper P 95.That​ is, find the hip breadth for men that separates the smallest 95​%from the largest 5​%.

Answer 1

Upper P95 = 16.21in

Explanation:

When the distribution is normal, we use the z-score formula.

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

`Z = (X - \mu)/(\sigma)`

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 question, we have that:

`\mu = 14.4, \sigma = 1.1`

Upper P 95

This is the 95th percentile, which is X when Z has a pvalue of 0.95. So X when Z = 1.645.

Then

`Z = (X - \mu)/(\sigma)`

`1.645 = (X - 14.4)/(1.1)`

`X - 14.4 = 1.1*1.645`

`X = 16.21`

Upper P95 = 16.21in