(1 point) The scores of students on the SAT college entrance examinations at a c

Question

(1 point) The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean A:: 538.4 and standard deviation 26.4. (a) What is the probability that a single student randomly chosen from all those taking the test scores 544 or higher? ANSWER: 416006 For parts (b) through (d), consider a simple random sample (SRS) of 25 students who took the test. (b) What are the mean and standard deviation of the sample mean score , of 25 students? The mean of the sampling distribution for is: The standard deviation of the sampling distribution for is (c) What z-score corresponds to the mean score of 544 ANSWER (d) What is the probability that the mean score of these students is 544 or higher? ANSWER: ESE

Explanation / Answer

b) mean of the sampling disribution = population mean = 538.4

standard deviation of sampling distribution = population standard deviation / sqrt(n) = 26.4 / sqrt(25) = 5.28

c) Z score of 544 = (544 - 538.4) / 5.28 = 1.06

d) P(mean score is higher than 544) = P(Z > 1.06) = 1 - P(Z < 1.06) = 1 - 0.8554 = 0.1446

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