Question

The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth-graders. Scores on the test range from 0 to 500. Suppose that you give the NAEP test to an SRS of 1089 eighth-graders from a large population in which the scores have mean μ = 287 and standard deviation σ = 125. The mean x will vary if you take repeated samples. The sampling distribution of x is approximately Normal. It has mean μ = 287. What is its standard deviation?

Answer 1

Answer:

Its standard deviation is 3.79.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

$\sigma = 125, n = 1089$

So

$s = \frac{125}{\sqrt{1089}} = 3.79$

Its standard deviation is 3.79.