The daily revenue at a university snack bar has been recorded for the past five years. Records indicate that the mean daily revenue is $2700 and the standard deviation is $400. The distribution is skewed to the right due to several high volume days (football game days). Suppose that 100 days are randomly selected and the average daily revenue computed. Which of the following describes the sampling distribution of the sample mean?
A) normally distributed with a mean of $2700 and a standard deviation of $40
B) normally distributed with a mean of $2700 and a standard deviation of $400
C) normally distributed with a mean of $270 and a standard deviation of $40
D) skewed to the right with a mean of $2700 and a standard deviation of $400

Question

Quizplus · Accepted Answer

The central limit theorem states that the sampling distribution of the sample mean will be approximately normal, regardless of the shape of the population distribution. The mean of the sampling distribution will be equal to the mean of the population, and the standard deviation of the sampling distribution will be equal to the standard deviation of the population divided by the square root of the sample size. In this case, the mean of the population is $2700 and the standard deviation of the population is $400. The sample size is 100, so the standard deviation of the sampling distribution will be $400 / sqrt(100) = $40. Therefore, the sampling distribution of the sample mean will be normally distributed with a mean of $2700 and a standard deviation of $40.

The Daily Revenue at a University Snack Bar Has Been