Question

It is known that the length of time that people wait for a city bus to arrive is right skewed with mean 6 minutes and standard deviation 4 minutes. A sample of 25 wait times is randomly selected. What is the standard deviation of the sampling distribution of the sample wait times

Answer 1

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 $\mu$ and standard deviation $\sigma$, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

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 $\sigma = 4$

A sample of 25 wait times is randomly selected.

This means that $n = 25$

What is the standard deviation of the sampling distribution of the sample wait times?

$s = \frac{4}{\sqrt{25}} = 0.8$

The standard deviation of the sampling distribution of the sample wait times is of 0.8 minutes.