The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ = 542.9 and standard deviation o - 28.4. (a) What is the probability that a single student randomly chosen from all those taking the test scores 547 or higher? ANSWER: 0.4426 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 , of 35 students? The mean of the sampling distribution for is: 542.9 The standard deviation of the sampling distribution for is: 4.8005 (c) What z-score corresponds to the mean score of 547? ANSWER: 0.8541 (d) What is the probability that the mean score of these students is 547 or higher? ANSWER: 0.20

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