Chapter 8.5, Problem 14E

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

Chapter
Section

### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336
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 Î¼=69.0 .

The standard deviation is Ïƒ=2.8â€‰inches .

Calculation:

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

f(x)=1Ïƒ2Ï€eâˆ’(xâˆ’Î¼)22Ïƒ2 (1)

Substitute 69.0 for Î¼ and 2.8 inches for Ïƒ in Equation (1).

f(x)=12.82Ï€eâˆ’(xâˆ’69)22Ã—2.82=17.02eâˆ’(x2âˆ’138x+4,761)15.68

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

P(65â‰¤Xâ‰¤73)=âˆ«6573f(x)â€‰dx=âˆ«6573(17

(b)

To determine

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

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