The scores of individual students on the American College Testing (ACT) composite college entrance examination have a normal distribution with a mean of 17.3 and a standard deviation of 7.5. Please explain the steps.

(a) What is the probability that a single student is randomly chosen from all those taking the test with scores of 25 or higher? 0.1515

(b) Now take an SRS of 68 students who took the test. What is the mean and standard deviation of the average (sample mean) score for the 68 students? (Round the standard deviation to 3 decimal places). x = 17.3 x = ?

(c) What is the probability that the mean score x of these 68 students is 18.76 or higher

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