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The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test...

The scores of 12th-grade students on the National Assessment of Educational Progress year 2000 mathematics test have a distribution that is approximately Normal with mean μ = 300 and standard deviation σ = 35.

(a) Choose one 12th-grader at random. What is the probability that his or her score is higher than 300? Higher than 335?

(b) Now choose an SRS of four 12th-graders and calculate their mean score x. If you did this many times, what would be the mean and standard deviation of all the x-values?

(c) What is the probability that the mean score for your SRS is higher than 300? Higher than 335?

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