Before taking a preparatory course for a common standardized college aptitude test, and the scores for high school students on the exam are normally distributed with a mean of 519 and a standard deviation of 102. Randomly selected men are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the test has no effect. In other words, assume that the mean would still be

=

519

=519

and the standard deviation would still be

=

102

=102

for those after taking the prep course. Then

Round your answer to 4 decimal places.

(a)If one high school student who took the course is randomly selected, find the probability that his/her score is at least 592.2.

(b)If 7 high school students that took the course are randomly selected, find the probability that their mean score is at least 592.2.

(c)Is there strong evidence to support the claim that the course is actually effective?

• Yes. The probability indicates that it is (highly ?) unlikely that by chance, a randomly selected group of students would get a mean as high as 592.2.
• No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 592.2.