Question

A population has a mean muequals160 and a standard deviation sigmaequals20. Find the mean and standard deviation of the sampling distribution of sample means with sample size nequals58

Answer 1

Answer:

Mean 160

Standard deviation 2.63

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:

$\mu = 160, \sigma = 20$

Find the mean and standard deviation of the sampling distribution of sample means with sample size n = 58.

Mean 160

Standard deviation $s = \frac{20}{\sqrt{58}} = 2.63$