Question

Random samples of size 64 are taken from an infinite population whose mean and standard deviation are 24 and 6.4, respectively. The distribution of the population is unknown.
What are the mean and the standard error of the sample mean?

Answer 1

Answer:

Mean 24, standard error 0.8

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, also called standard error $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 24, \sigma = 6.4, n = 64$

What are the mean and the standard error of the sample mean?

By the Central Limit Theorem, mean 24 and standard error $s = \frac{6.4}{\sqrt{64}} = 0.8$