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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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Women’s Height The mean height of American women (from 30 to 39 years old) is 64 inches, and the standard deviation is 3 inches. Use a symbolic integration utility or a graphing utility to find the probability that a 30- to 39-year-old woman chosen at random is

(a) between 5 and 6 feet tall.

(b) 5 feet 8 inches or taller.

(c) 6 feet or taller.

(Source: U.S. National Center for Health Statistics)

(a)

To determine

To calculate: The probability for the women chosen from the American population of age group 30-to 39 year old people which were between 5 feet and 6 feet tall.

Explanation

Given Information:

Standard deviation is 3 inches, the mean height of American women from 30-39-year age group is 64 inches.

Formula used:

The relation between feet and inches is,

1 feet=12 inches

Calculation:

Convert height 5 feet into inches as,

(5 feet)(12 inches1feet)=60 inches

Convert height 6 feet into inches.

(6 feet)(12 inches1feet)=72 inches

The mean value of the length of the American women is 64 inches.

Use excel to find the probability. Steps to use excel is as follows:

Step 1: Add the function “NORM.DIST” in the excel.

Step 2: Add the values of the “x”, mean, standard deviation and cumulative as “=NORM.DIST(60,64,3, TRUE)” in the cell as shown in the below snip.

(b)

To determine

To calculate: The probability for the women chosen from the American population of age group 30-to 39 year old people who are 5 feet 8 inches or taller.

(c)

To determine

To calculate: The probability for the women chosen from the American population of age group 30-to 39 year old people which were 6 feet or taller.

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