Question

Engineers must consider the breadths of male heads when designing helmets. The company researchers have determined that the population of potential clientele have head breadths that are normally distributed with a mean of 7.1-in and a standard deviation of 1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head breadths that are in the smallest 1.5% or largest 1.5%. What is the minimum head breadth that will fit the clientele? min - What is the maximum head breadth that will fit the clientele? max- Enter your answer as a number accurate to 1 decimal place.

Answer 1

solution:-

given that mean = 7.1 , standard deviation = 1

here given that smallest 1.5% or largest 1.5%

the z-value corresponds to the given probability value of 1.5% = 0.015 from standard normal table is

for left of z = -2.17 and right of z = 2.17

=> the minimum head breadth that will fit the clientele

=> z = (x-mean)/standard deviation

= x = z*standard deviation + mean

=> x = -2.17*1+7.1

=> x = 4.9

minimum value = 4.9

=> the miximum head breadth that will fit the clientele

=> z = (x-mean)/standard deviation

= x = z*standard deviation + mean

=> x = 2.17*1+7.1

=> x = 9.3

maximum value = 9.3