The prices of pants at a large clothing store chain are skewed left with a mean of $32 and a standard deviation of $20. 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
skewed left with a mean of 32 and standard deviation of 6.32
B
skewed left with a mean of 32 and a standard deviation of 20
C
approximately Normal with a mean of 32 and a standard deviation of 20
D
approximately Normal with a mean of 32 and a standard deviation of 6.32
Explanation
The sampling distribution has a mean equal to the population mean, $32. Its standard deviation (the standard error) is $20/√10 ≈ $6.32. Since the population prices are skewed left and a sample size of 10 is not large enough to guarantee an approximately Normal sampling distribution, the best description is skewed left with a mean of 32 and a standard deviation of 6.32.
AI-written and checked against the verified answer.