A teacher knows that scores on one of her tests are heavily left skewed, with a mean score of 78 and a standard deviation of 18. She randomly selects 15 grades and records the mean score. What is the shape of the distribution of the sample mean for all possible random samples of size 15 from this population?

The sample size is only 15, which is not large enough to rely on the Central Limit Theorem to make the sample-mean distribution approximately Normal when the population is heavily skewed. Instead, with a small sample, the distribution of the sample mean will retain much of the population’s left skew. So the distribution is skewed left.

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