Question

A population has a mean muequals71 and a standard deviation sigmaequals24. Find the mean and standard deviation of a sampling distribution of sample means with sample size nequals64.

Answer 1

Mean 71

Standard deviation 3

Explanation:

We use the Central Limit Theorem to solve this question.

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

In this problem, we have that:

`\mu = 71, \sigma = 24, n = 64`. So

Mean 71

Standard deviation
`s = (24)/(√(64)) = 3`