Engineers want to design seats in commercial aircraft so that they are wide enou

Question

Engineers want to design seats in commercial aircraft so that they are wide enough to fit 90% 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 14.7 in. and a standard deviation of 1.1 in. Find P_90. That is, find the hip breadth for men that separates the smallest 90% from the largest 10%. The hip breadth for men that separates the smallest 90% from the largest 10% is P_90 = in.

Explanation / Answer

From information given, z=0.27, Xbar=14.7, s=1.1. Substitute the values in following z score equation to obtain the Xi.

z=(Xi-Xbar)/s

0.27=(Xi-14.7)/1.1

Xi=14.997~15 in.

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