Question

The mean is 47.1 and the standard deviation is 9.5 for a population. Using the Central Limit Theorem, what is the standard deviation of the distribution of sample means for samples of size 60

Answer 1

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.

Explanation:

Central Limit Theorem

The Central Limit Theorem establishes 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.

Standard deviation is 9.5 for a population.

This means that
`\sigma = 9.5`

Sample of 60:

This means that
`n = 60`

What is the standard deviation of the distribution of sample means for samples of size 60?

`s = (\sigma)/(√(n)) = (9.5)/(√(60)) = 1.2264`

The standard deviation of the distribution of sample means for samples of size 60 is of 1.2264.