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.

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