The prices of pants at a large clothing store chain are skewed left with a mean of 32 dollars and a standard deviation of 20 dollars The manager at one of the stores randomly selects 10 pairs of pants. Which of the following best describes the sampling distribution of all possible samples of size 10 ?
Answer
A
approximately Normal with a mean of 32 and a standard deviation of 20
B
approximately Normal with a mean of 32 and a standard deviation of 6 point 3 2
C
skewed left with a mean of 32 and standard deviation of 6 point 3 2
D
skewed left with a mean of 32 and a standard deviation of 20
Explanation
For samples of 10, the sampling distribution of the sample mean has mean 32 dollars and standard deviation 20/√10 ≈ 6.32 dollars. Because the population prices are skewed left and a sample size of 10 is not large enough to guarantee an approximately Normal distribution, the sampling distribution is best described as skewed left.
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