Courtney would like to estimate the net worth of all people in the US. The distribution of net worth of people in the US is strongly skewed to the right. Courtney selects an SRS of size n = 15 from this population and calculates the sample mean. What is the shape of the distribution of the sample mean for all possible simple random samples of size 15 from this population?

With a small sample size of 15, the Central Limit Theorem does not guarantee that the sample-mean distribution is approximately Normal when the population is strongly skewed. The sample means will generally retain the population’s right skew, though the skew may be less pronounced. Therefore, the distribution is skewed to the right.

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