Question

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 $3250 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 60 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?

Group of answer choices

normally distributed with a mean of $3250 and a standard deviation of $400

skewed to the right with a mean of $3250 and a standard deviation of $400

normally distributed with a mean of $325 and a standard deviation of $58.09.

normally distributed with a mean of $3250 and a standard deviation of $58.09.

Answer 1

We know that,

The central limit theorem states that if you have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement , then the distribution of the sample means will be approximately normally distributed with mean μ and standard deviation σ/squareroot(n)

Hence,

Required correct answer is,

normally distributed with a mean of $3250 and a standard deviation of $58.09.

i.e., Last option is correct.

Thank you.