Chapter 1.1, Problem 25E

(a)

To determine

To calculate the percentage of respondents whose weight is about right.

Answer to Problem 25E

71.25%

Explanation of Solution

Given:

The Dataset:

			Gender
		Female	Male	Total
	About right	560	295	855
Body image	Overweight	163	72	235
	Underweight	37	73	110
	Total	760	440	1200

Calculation:

The number of respondents with the body weight about right are = 855

Total number of respondents are = 1200

  $\begin{array}{c}\text{Proportion of respondants with =}\frac{\text{855}}{1200}\\ =0.7125\\ =71.25\%\end{array}$

(b)

To determine

To calculate the proportion of female respondents.

Answer to Problem 25E

0.6333

Explanation of Solution

Calculation:

No. of female respondents = 760

Total no. of respondents = 1200

  $\begin{array}{c}\text{Proportion of female respondants = }\frac{\text{No}\text{. of female respondants}}{\text{Total no}\text{. of respondants}}\\ =\frac{760}{1200}\\ =0.6333\end{array}$

(c)

To determine

To calculate the percentage of respondents who are male and think that they are overweight or underweight.

Answer to Problem 25E

Required proportion = 0.5333

Explanation of Solution

Calculation:

No. of male respondents = 440

No. of overweight or underweight respondents = 345

No. of respondents who are male and overweight or underweight respondents = 72 + 73 = 145

Total no. of respondents = 1200

  $\begin{array}{l}\text{P}\left(\text{Male or overweight or underweight respondent}\right)\\ \text{= }\left[\begin{array}{l}\text{P(Male) + P(Overweight or underweight) }\\ \text{- P}\left(\text{Male and overweight or underweight respondent}\right)\end{array}\right]\\ =\frac{440}{1200}+\frac{345}{1200}-\frac{145}{1200}\\ =0.5333\end{array}$