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Scores for a common standardized college aptitude test are normally distributed with a mean of 499 and a standard deviation of 106. Randomly selected men are given a Test Prepartion Course before taking this test. a. If 1 of the men is randomly selected, find the probability that his score is at least 542.8. P(X> 542.8)- Enter your answer as a number accurate to 4 decimal places. b. If 15 of the men are randomly selected, find the probability that their mean score is at least 542.8. P> 542.8) Enter your answer as a number accurate to 4 decimal places. c. Is it unusual to obtain a mean score of more than 542.8 from a random sample of 15 men? Why or why not and how does this relate to the effectiveness of the Test Prep course? ONo. The probability is greater than 0.05 which indicates that is is not unlikely by chance alone. There is no sufficient evidence to determine if the course is effective. OYes. The probability is less than 0.05 which indicates that is is unlikely by chance alone to score higher than 542.8. It appears the coure is effective. License Points possible: 1 This is attempt 1 of 3 Post this question to forum

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From the given inform ati on, let X be the scores for a common standardized college aptitude test are normally distributed with μ-499, and σ-106 (a)The probability that his score is at least 542.8 is P(x2542 8) P5428- μ- fa ) 542.8-499 106 = P(72 0.4132) -1-P(Z <0.41) 1-0.6591 0.3409 (b)If 15 of the men are randomly selected, the probability that their mean score is at least 542.8 is P(72 5428)-PT-, 542.8-4) 542.8-μ 542.8-499 106 15 - P(Z 21.6) 1P(Z <1.6) by symmetric property 1-0.9452 0.0548 (c)No. The probability is greater than 0.05 which indicates that is not unlikely by chance alone. There is no sufficient evidence to determine if the course is effective

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