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%.

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 = %

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

step-by-step explanation: