Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 515 and a standard deviation of 110. Randomly selected students are given a Test Prepartion Course before taking this test. Assume, for sake of argument, that the course has no effect.

If 1 of the students is randomly selected, find the probability that their score is at least 581.7.
P(X > 581.7) =
Enter your answer as a number accurate to 4 decimal places.

If 17 of the students are randomly selected, find the probability that their mean score is at least 581.7.
P(¯¯¯XX¯ > 581.7) =
Enter your answer as a number accurate to 4 decimal places.

If the random sample of 17 students does result in a mean score of 581.7, is there strong evidence to support the claim that the course is actually effective?

• No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 581.7.
• 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 581.7.

Answer 1