Chapter 10.2, Problem 1.2CYU

To determine

To find: The shape of the sampling distribution of ${\overline{x}}_1-{\overline{x}}_2$

Answer to Problem 1.2CYU

It is approximately normally distributed.

Explanation of Solution

Given:

  $\begin{array}{l}\text{Sample mean}\left({\overline{x}}_1\right)=27\\ \text{Sample mean}\left({\overline{x}}_2\right)=17\\ \text{Standard deviation}\left({\sigma }_1\right)=0.8\\ \text{Standard deviation}\left({\sigma }_2\right)=0.5\end{array}$

Here, it has been provided that distributions of population are normal. Thus, it could be said that the sampling distribution of ${\overline{x}}_1-{\overline{x}}_2$ is approximately normally distributed.