According to a human modeling project, the distribution of foot lengths of 16- to 17-year-old boys is approximately Normal with a mean of 25.2 centimeters and a standard deviation of 1.5 centimeters. In the United States, a man's size 11 shoe fits a foot that is 27.9 centimeters long. What percentage of boys of this age group will wear a size 11 shoe or larger? The percentage of boys 16- to 17-years-old who wear a size 11 shoe or larger is nothing%.

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jacknjill jacknjill · Answer 1 · 2020-04-12T06:44:22+02:00

The percentage of boys 16- to 17-years-old who wear a size 11 shoe or larger is 3.59%.

Step-by-step explanation:

Step 1: Sketch the curve.

The probability that X>27.9 is equal to the blue area under the curve.

Step 2:

Since μ=25.2 and σ=1.5 we have:

P ( X > 27.9 ) = P ( X−μ > 27.9−25.2 )

⇒ P ( X−μ/σ > 27.9−25.2/1.5)

Since Z=x−μσ and 27.9−25.21.5=1.8 we have:

P ( X>27.9 )=P ( Z>1.8 )

Step 3: Use the standard normal table to conclude that:

P (Z>1.8)=0.0359

Percentage = [tex]0.0359(100) = 3.59[/tex]%

Therefore , The percentage of boys 16- to 17-years-old who wear a size 11 shoe or larger is 3.59%.

andromache andromache · Answer 2 · 2022-03-16T07:08:55+01:00

The percentage of boys 16- to 17-years-old who wear a size 11 shoe or larger is 3.59%.

Since there is the mean of 25.2 centimeters and a standard deviation of 1.5 centimeters.

Now

P ( X > 27.9 ) = P ( X−μ > 27.9−25.2 )

So,

P ( X−μ/σ > 27.9−25.2/1.5)

Since Z=x−μσ and 27.9−25.21.5=1.8

So,

P ( X>27.9 )=P ( Z>1.8 )

Here we use standard normal table

So,

P (Z>1.8)=0.0359

= 3.59%

hence, The percentage of boys 16- to 17-years-old who wear a size 11 shoe or larger is 3.59%.

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