Sales prices of baseball cards from the 1960s are known to possess a skewed-right distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale price of the selected cards.
A) normal with a mean of $5.25 and a standard error of $2.80
B) skewed-right with a mean of $5.25 and a standard error of $2.80
C) normal with a mean of $5.25 and a standard error of $0.28
D) skewed-right with a mean of $5.25 and a standard error of $0.28

Question

Quizplus · Accepted Answer

According to the central limit theorem, the sampling distribution of the sample mean will be normal if sample size is sufficiently large (n ≥ 30) regardless of the shape of the population distribution. Since the sample size is large enough (n = 100), the sampling distribution for the sample mean sale price will be normal with a mean of $5.25 and a standard error equal to the population standard deviation divided by the square root of the sample size, which is $2.80/sqrt(100) = $0.28. Therefore, answer C is correct.

Sales Prices of Baseball Cards from the 1960s Are Known