Chapter 6.2, Problem 52E

a.

To determine

To explain: The reason of assuming that scores of two students are not dependent.

Explanation of Solution

Given:

For women:

Population mean $\left(\mu \right)=120$

Population standard deviation $\left(\sigma \right)=28$

For men:

Population mean $\left(\mu \right)=105$

Population standard deviation $\left(\sigma \right)=35$

Calculation:

From the provided information, it is known that the sample have been chosen randomly. Thus, it is required to assume that scores of men and women are independent.

b.

To determine

To find: The expected value and standard deviation of the scores of men and women.

Answer to Problem 52E

The expected value and standard deviation are 15 and 44.8219.

Explanation of Solution

The expected value and standard deviation of the scores of men and women can be computed as:

  $\begin{array}{c}{\mu }_{F-M}={\mu }_F-{\mu }_M\\ =120-105\\ =15\end{array}$

  $\begin{array}{c}{\sigma }_{F-M}=\sqrt{{\sigma }^2{}_F-{\sigma }^2{}_M}\\ =\sqrt{{28}^2+{35}^2}\\ =\sqrt{2009}\\ =44.8219\end{array}$

The expected value and standard deviation are 15 and 44.8219.

c.

To determine

To find: Whether the probability that women has scores more than man can be calculated or not.

Explanation of Solution

The probability that women has scores more than man cannot be calculated because no information regarding the distribution has been provided. Thus, the required probability cannot be computed here.