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

Its standard deviation is 3.79.

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 = (\sigma)/(√(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 = (125)/(√(1089)) = 3.79`

Its standard deviation is 3.79.