Question

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

9999​%

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

14.814.8  

in. and a standard deviation of

1.11.1

in. Find

Upper P 99P99.

That​ is, find the hip breadth for men that separates the smallest

9999​%

from the largest

11​%.

Answer 1

Solution :

Given that,  

mean = = 14.8

standard deviation = = 1.1

Using standard normal table ,

P(Z < z) = 99%

P (Z < z) = 0.99

P(Z < 2.33) = 0.99

z = 2.33

Using z-score formula,

x = z * +

x = 2.33* 1.1 + 14.8 = 17.36

the hip breadth for men that separates the smallest 99% is 17.36