Answer:
The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes 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. Otherwise, the mean and the standard deviations holds, but the distribution will not be approximately normal.
Standard deviation 4 minutes.
This means that [tex]\sigma = 4[/tex]
A sample of 25 wait times is randomly selected.
This means that [tex]n = 25[/tex]
What is the standard deviation of the sampling distribution of the sample wait times?
[tex]s = \frac{4}{\sqrt{25}} = 0.8[/tex]
The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.
