AnswersNC-Math 4Sampling Distribution of the Sample MeanQuestion 3
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Sampling Distribution of the Sample Mean

Question 3 • NC-Math 4

The daily temperatures for the winter months in Virginia are Normally distributed with a mean of 59°F and a standard deviation of 10°F. A random sample of 10 temperatures is taken from the winter months and the mean temperature is recorded. What is the shape of the distribution of the sample mean for all possible random samples of size 10 from this population?

Answer
A
skewed left
B
skewed right
C
approximately Normal
D
approximately uniform

Explanation

The population temperatures are Normally distributed, so the sampling distribution of the sample mean is Normal for any sample size. Here, that means the averages from all possible samples of 10 temperatures have an approximately Normal shape. The correct choice is C, approximately Normal.

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