Question

Test scores for high school graduates who took the SAT in 2018 during their final year of high school are normally

distributed with a mean score of 1068 and a standard deviation of 204 (based on data from the College Board). In
2018, a random sample of 25 high school seniors were selected and given the Columbia Review course before taking
the SAT test. Assume the course has no effect on scores.
a. If 1 high school graduate is randomly selected, find the probability that his or her score on the SAT is at least
1130.
b. If 25 high school graduates are randomly selected, find the probability that their mean score is at least 1130.
c. In finding the probability for part (b), why can the central limit theorem be used even though the sample
size does not exceed 30?

Answer 1

A. The probability that a randomly selected high school graduate scored at least 1130 on the SAT is about 62%.

b. The probability that the mean score of 25 randomly selected high school graduates is at least 1130 is about 16%.

c. The central limit theorem says that if you take a large enough sample from a population, the distribution of the sample means will be normally distributed, even if the population distribution is not normally distributed. In this case, the sample size of 25 is large enough, so we can use the central limit theorem to find the probability.

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