Answer:
The standard deviation of the sample mean is 4 minutes
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this problem, we have that:
The standard deviation of the population is 32.
Sample of 64.
So
[tex]s = \frac{32}{\sqrt{64}} = 4[/tex]
The standard deviation of the sample mean is 4 minutes
