Question

Engineers must consider the width of male heads when designing helmets for men. The company researchers have determined that the population of potential clientele have head widths that are normally distributed with a mean of 6.1-in and a standard deviation of 1.1-in. Due to financial constraints, the helmets will be designed to fit all men except those with head widths that are in the smallest 7.1% or largest 7.1%.

What is the maximum head width that can wear this company's helmet?

Solve this problem by hand showing all steps. Do not use StatCrunch. Use the Standard Normal Table [LINK] to find all probabilities or unknown values. Your answer should be rounded to one decimal place. Write your answer in a complete sentence form. Be sure to watch the following video for information on how to write up the problem with correct notation, defining variables, etc.

Answer 1

Solution:-

Given that,

mean = = 6.1

standard deviation = = 1.1

Using standard normal table,

P(Z < z) = 7.1%

= P(Z < z) = 0.071  

= P(Z < -1.47) = 0.071

z = -1.47

Using z-score formula,

x = z * +

x = -1.47 * 1.1 + 6.1

x = 4.5 in.

Using standard normal table,

P(Z > z) = 7.1%

= 1 - P(Z < z) = 0.071  

= P(Z < z) = 1 - 0.071

= P(Z < z ) = 0.929

= P(Z < 1.47 ) = 0.929  

z = 1.47

Using z-score formula,

x = z * +

x = 1.47 * 1.1 + 6.1

x = 7.7 in.

maximum head width = 7.7 in.