Question

Engineers must take into account the width of men's heads when designing motorcycle helmets. The width of men's heads is normally distributed, with a mean of 6.0 inches and a standard deviation of 1.0 inch. Due to economic limitations, helmets will be designed to fit all men, except 2.5% with smaller widths and 2.5% with larger widths. Calculate the minimum and maximum head widths that will fit the helmets.

Answer 1

Solution:

Given that,

mean = = 6.0

standard deviation = = 1.0

Using standard normal table,

a ) P(Z < z) = 2.5%

P(Z < z) = 0.025

P(Z < - 0.61) =0.025

z = -1.96

Using z-score formula,

x = z * +

x = -1.96 * 1.0 +6.0

x = 4.04

The minimum = 4.04

b ) P( Z > z) = 2.5%

P(Z > z) = 0.025

1 - P( Z < z) = 0.025

P(Z < z) = 1 - 0.025

P(Z < z) = 0.975

z = - 0.41

Using z-score formula,

x = z * +

x = 1.96 * 1.0 + 6.0

x = 7.96

The maximum = 7.96