Question

1) Scores for a common standardized college aptitude test are normally distributed with a mean of 495 and a standard deviation of 108. 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 551.9.
P(X > 551.9) =  
Enter your answer as a number accurate to 4 decimal places.

If 13 of the men are randomly selected, find the probability that their mean score is at least 551.9.
P(M > 551.9) =  
Enter your answer as a number accurate to 4 decimal places.

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 13 men does result in a mean score of 551.9, 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 551.9.
• No. The probability indicates that it is too possible by chance alone to randomly select a group of students with a mean as high as 551.9.

2) Scores for a common standardized college aptitude test are normally distributed with a mean of 495 and a standard deviation of 115. 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 528.4.
P(X > 528.4) =  
Enter your answer as a number accurate to 4 decimal places.

If 20 of the men are randomly selected, find the probability that their mean score is at least 528.4.
P(M > 528.4) =  
Enter your answer as a number accurate to 4 decimal places.

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 20 men does result in a mean score of 528.4, 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 528.4.
• 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 528.4.

Answer 1