Answer:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Solution to the problem
Let X the random variable of interest for a population. We know from the problem that the distribution for the random variable X is given by:
We take a sample of n=64 . That represent the sample size.
The sample mean is defined as:
And if we find the expected value and variance for the sample mean we got:
Var(\bar X) = \frac{\sigma^2}{n}[/tex]
The distribution for the sample mean is given by: