Question

A design studio is planning on producing work desks. Their chair needs to be adjustable enough to accommodate the "sitting knee heights” of the 5th percentile of women and the 95th percentile of men. Males have sitting knee heights that are normally distributed with a mean fo 21.4 in and a standard deviation of 1.2 in and females have sitting knee heights that are normally distributed with a mean of 19.6 in and a standard deviation of 1.1 inches. What range of knees heights do these desks need to accommodate?

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

Let the 5th percentile of women sitting knee height be M and 95th percentile of men sitting knee height be N.

P(X < M) = 0.05

P(Z < (M - 19.6)/1.1) = 0.05

Take the value of Z corresponding to 0.05 from standard normal distribution table

(M - 19.6)/1.1 = -1.645

M = 17.79 in

P(X < N) = 0.95

P(Z < (N - 21.4)/1.2) = 0.95

(N - 21.4)/1.2 = 1.645

N = 21.41 in

The range of knees heights these desks need to accommodate is 17.79 in to 21.41 in.