Question

Suppose a researcher is studying a population that has a mean of μ=38.6 and a standard deviation of σ=1.1. The researcher studies a simple random sample of size n = 200. According to the central limit theorem, what is the approximate standard deviation of the sampling distribution of the mean? Round the answer to the nearest thousandth if needed.

Answer 1

The approximate standard deviation of the sampling distribution of the mean is 0.078

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:

`\sigma = 1.1, n = 200`.

According to the central limit theorem, what is the approximate standard deviation of the sampling distribution of the mean?

`s = (1.1)/(√(200)) = 0.078`

The approximate standard deviation of the sampling distribution of the mean is 0.078