   Chapter 8.5, Problem 14E

Chapter
Section
Textbook Problem

According to the National Health Survey, the heights of adult males in the United States are normally distributed with mean 69.0 inches and standard deviation 2.8 inches. (a) What is the probability that an adult male chosen at random is between 65 inches and 73 inches tall ? (b) What percentage of the adult male population is more than 6 feet tall ?

(a)

To determine

To find: The probability that an adult male chosen at random is between 65 inches and 73 inches tall.

Explanation

Given information:

The height of the adult male is normally distributed.

The mean value is μ=69.0 .

The standard deviation is σ=2.8inches .

Calculation:

Find the probability density function for normal distribution as shown below.

f(x)=1σ2πe(xμ)22σ2 (1)

Substitute 69.0 for μ and 2.8 inches for σ in Equation (1).

f(x)=12.82πe(x69)22×2.82=17.02e(x2138x+4,761)15.68

Find the probability that an adult male chosen at random is between 65 inches and 73 inches tall. P(65X73) as shown below.

P(65X73)=6573f(x)dx=6573(17

(b)

To determine

To find: The percentage of the adult male population is more than 6 feet tall.

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

Convert the expressions in Exercises 6584 to power form. 35x5x8+72x3

Finite Mathematics and Applied Calculus (MindTap Course List)

limx(lnx)1/x= a) 0 b) 1 c) e d)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

What are the five steps of the scientific method?

Research Methods for the Behavioral Sciences (MindTap Course List) 