Question

Scores on the SAT college entrance test in a recent year were roughly Normal with mean 1012.5 and standard deviation 184.9. You choose an SRS of 90 students and average their SAT scores. If you do this many times, the mean of the average scores you get will be close to

Answer 1

By the Central Limit Theorem, the mean of the average scores you get will be close to 1012.5.

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.

Mean score of the population:

1012.5

If you do this many times, the mean of the average scores you get will be close to

By the Central Limit Theorem, the mean of the average scores you get will be close to 1012.5.