Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 480 and a standard deviation of 104. 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 527. P(X > 527) =

If 11 of the men are randomly selected, find the probability that their mean score is at least 527. P(M > 527) =

. 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 11 men does result in a mean score of 527, 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 527.

or

No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 527.

Answer 1

Here scores for a common standardized college aptitude test are normally distributed with a mean of 480 and a standard deviation of 104.

We need to find

As distribution is normal we can convert x to z

Now for sample size n=11, we need to find

P(M > 527)

As population is normal, as per central limit theorem M is also normally distributed with mean=480 and standard deviation=

As distribution is normal we convert M to z

As P(M>527)>0.05

Answer is No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 527.