Question

IQ scores are normally distributed with a mean of 105 and a standard deviation of 17. Assume that many samples of size n are taken from a large population of people and the mean IQ score is computed for each sample. If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.

Answer 1

Mean 105

Standard deviation 1.89

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sample means with size n of at least 30 can be approximated to a normal distribution with mean
`\mu` and standard deviation
`s = (\sigma)/(√(n))`

In this problem, we have that:

`\mu = 105, \sigma = 17`

If the sample size is n 81, find the mean and standard deviation of the distribution of sample means.

By the Central limit theorem

mean 105

Standard deviation

`s = (17)/(√(81)) = 1.89`