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In: Statistics and Probability

The scores of students on the SAT college entrance examinations at a certain high school had...

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean ?=545.8μ=545.8 and standard deviation ?=28.4σ=28.4.

(a) What is the probability that a single student, randomly chosen from all those taking the test, would score 552 or higher?

For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.

(b) What are the mean and standard deviation of the sample mean score ?¯x¯, of 35 students?

Mean: Standard deviation:

(c) What z-score corresponds to the mean score ?¯x¯ of 552?

(d) What is the probability that the mean score ?¯x¯ of these students is 552 or higher?

(e) Suppose that you want to test whether the mean SAT score is higher for students who take an SAT prep course. You take a random sample of 35 students who have taken an SAT prep course, and find that the sample mean score is 552. What is the p-value for this study?

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