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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270336

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BuyFindarrow_forward

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.

  1. (a) What is the probability that an adult male chosen at random is between 65 inches and 73 inches tall ?
  2. (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.

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