The prices of houses in the US are strongly skewed to the right with a mean of $383,500 and a standard deviation of $289,321. A real estate agent takes a random sample of 10 houses and records the mean price. What is the shape of the distribution of the sample mean for all possible random samples of size 10 from this population?

With a sample size of 10, the Central Limit Theorem does not guarantee that the distribution of sample means is approximately Normal; that generally requires a larger sample when the population is strongly skewed. The sample-mean distribution will still tend to reflect the population’s strong right skew, though it will be less variable. Therefore, the distribution is skewed right.

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