Scores for a common standardized college aptitude test are normally distributed with a mean of 499 and a standard deviation of 95. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the test has no effect. If 1 of the men is randomly selected, find the probability that his score is at least 543.8. P(X > 543.8) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. If 18 of the men are randomly selected, find the probability that their mean score is at least 543.8. P(M > 543.8) = Enter your answer as a number accurate to 4 decimal places. NOTE: Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted. If the random sample of 18 men does result in a mean score of 543.8, is there strong evidence to support the claim that the course is actually effective?

• Yes. The probability indicates that is is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 543.8.
• No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 543.8.