Engineers must consider the diameters of heads when designing helmets. The company researchers have determined that the population of potential clientele have head diameters that are

Question

Engineers must consider the diameters of heads when designing helmets. The company researchers have determined that the population of potential clientele have head diameters that are normally distributed with a mean of 6.4-in and a standard deviation of 1.2-in. Due to financial constraints, the helmets will be designed to fit all men except those with head diameters that are in the smallest 2.8% or largest 2.8%.

What is the minimum head diameter that will fit the clientele?

min =

What is the maximum head diameter that will fit the clientele?

max =

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer 1

z = x - mean / SD

x = head size

mean = 6.4

SD = 1.2

z for lowest 2.8% is -1.91

-1.91 = (x - 6.4)/1.2

x = 4.108

minimum head size 4.108 inches

because normal distribution is symmetric, z for highest 2.8% is 1.91

1.91 = (x - 6.4)/1.2

x = 8.692

minimum head size 8.692 inches