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

Answer:

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

Step-by-step 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 $s = \frac{\sigma}{\sqrt{n}}$

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?

$s = \frac{1.1}{\sqrt{200}} = 0.078$

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