Question

The daily revenue at a university snack bar has been recorded for the past five years. Records indicate that the mean daily revenue is $1,500 and the standard deviation is $500. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 110 days are randomly selected and the average daily revenue computed.
a. The sampling distribution has a mean of $1,500 and a standard deviation of $ __________.
Round your answer if needed to two decimal places.

Answer 1

Answer:

The sampling distribution has a mean of $1,500 and a standard deviation of $47.67

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 $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\sigma = 500, n = 110$

So

$s = \frac{500}{\sqrt{110}} = 47.67$

The sampling distribution has a mean of $1,500 and a standard deviation of $47.67