Chapter 7, Problem AP2.3CPT

To determine

To find: the distribution of sample means IQ score is.

Answer to Problem AP2.3CPT

Approximately normal with mean 122 and standard deviation 0.35

Explanation of Solution

Given:

  $\begin{array}{l}\mu =\text{122}\\ \sigma \text{=5}\\ n\text{=200}\end{array}$

Formula used:

  ${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}$

Calculation:

Sample size is greater than 30. By the central limit theorem, know that the sampling distribution of the sample mean $\overline{x}$ is about normal.

  $\mu \overline{x}=\mu =122$

  ${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}=\frac{5}{\sqrt{200}}=0.35$

Therefore the sampling distribution of the sample mean is about to normal with mean $122$ and standard deviation $0.35$ .

Hence, the correct option is (e)