Chapter 12, Problem AP4.25CPT

To determine

To explain which of the following statements about the sampling distribution of the sample mean weight $\overline{x}$ is true.

Answer to Problem AP4.25CPT

Option (d) is the correct option.

Explanation of Solution

In the question, suppose that the mean weight of a certain breed of pig is $280$ pounds with the standard deviation of $80$ pounds. The distribution of weight for these pigs tends to be somewhat skewed to the right. Thus, the distribution will be approximately normal distributed. We cannot say that the distribution is exactly normally distributed but since $n>30$ , we can say that by the central limit theorem the distribution is approximately normal. Thus, also,

  $\begin{array}{l}\sigma =\frac{80}{\sqrt{100}}\\ =8\\ \mu =280\end{array}$

Therefore, option (d) is the correct option.