Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 510 and a standard deviation of 98. Randomly selected men are given a Test Preparation Course before taking this test. Assume, for sake of argument, that the preparation course has no effect.

If 1 of the men is randomly selected, find the probability that his score is at least 588.4.
P(X > 588.4) =

If 9 of the men are randomly selected, find the probability that their mean score is at least 588.4.
P(M > 588.4) =

Assume that any probability less than 5% is sufficient evidence to conclude that the preparation course does help men do better. If the random sample of 9 men does result in a mean score of 588.4, 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 588.4.
• 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 588.4.

Answer 1

P(X > 588.4)

= P((X - )/ > (588.4 - )/)

= P(Z > (588.4 - 510)/98)

= P(Z > 0.8)

= 1 - P(Z < 0.8)

= 1 - 0.7881

= 0.2119

P(M > 588.4)

= P((M - )/() > (588.4 - )/())

= P(Z > (588.4 - 510)/(98/))

= P(Z > 2.4)

= 1 - P(Z < 2.4)

= 1 - 0.9918

= 0.0082

Yes, The probability indicates that is unlikely that by chance, a randomly selected group of students would get a mean as high as 588.4