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 14.7 in. and a standard deviation of 1.1 in. Find Upper P 95 That​ is, find the hip breadth for men that separates the smallest 95​% from the largest 5%.

The hip breadth for men that separates the smallest 95% from the largest 5​% is Upper P 95 =

Answer 1

Solution :

Given that,

mean = = 14.7

standard deviation = = 1.1

P( Z > z) = 95%

P(Z > z) = 0.95

1 - P( Z < z) = 0.95

P(Z < z) = 1 - 0.95

P(Z < z) = 0.05

z = -1.64

Using z-score formula,

x = z * +

x = -1.64 * 1.1 + 14.7

x = 12.896

P₉₅ = 12.90