The heights of a species of plant are approximately Normally distributed, have a mean of 9.31 cm, and have a standard deviation of 0.55 cm. If 20 of the plants are randomly selected, what is the probability that the mean plant height is less than 9.5 cm?

For a sample of 20 plants, the sampling distribution of the mean has standard error 0.55/√20 ≈ 0.123 cm. The z-score for a mean of 9.5 cm is (9.5 − 9.31)/0.123 ≈ 1.54. The probability of being below z = 1.54 is about 0.9388, so the answer is C, 0.9388.

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