Question

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​%.

Answer 1

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 = $0.0359(100) = 3.59$%

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