The amount of money collected by a snack bar at a large university has been recorded daily for the past five years. Records indicate that the mean daily amount collected is $6000 and the standard deviation is $400. The distribution is skewed to the right due to several high volume days (including football game days). Suppose that 100 days were randomly selected from the five years and the average amount collected from those days was recorded. Which of the following describes the sampling distribution of the sample mean?
A) normally distributed with a mean of $6000 and a standard deviation of $400
B) skewed to the right with a mean of $6000 and a standard deviation of $400
C) normally distributed with a mean of $600 and a standard deviation of $40
D) normally distributed with a mean of $6000 and a standard deviation of $40

Question

Quizplus · Accepted Answer

The Central Limit Theorem states that the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution, if the sample size is sufficiently large (usually n > 30). The mean of the sampling distribution will be equal to the population mean ($6000), and the standard deviation of the sampling distribution (standard error) is equal to the population standard deviation ($400) divided by the square root of the sample size (sqrt(100) = 10), which equals $40.

The Amount of Money Collected by a Snack Bar at a Large