Question

Scores for a common standardized college aptitude test are normally distributed with a mean of 482 and a standard deviation of 106. Randomly selected men are given a Prepartion Course before taking this test. Assume, for sake of argument, that the Preparation Course has no effect on people's test scores.

If 1 of the men is randomly selected, find the probability that his score is at least 544.3.
P(X > 544.3) =
Enter your answer as a number accurate to 4 decimal places.

If 14 of the men are randomly selected, find the probability that their mean score is at least 544.3.
P(x-bar > 544.3) =
Enter your answer as a number accurate to 4 decimal places.

If the random sample of 14 men does result in a mean score of 544.3, is there strong evidence to support a claim that the Preapartion Course is actually effective? (Use the criteria that "unusual" events have a probability of less than 5%.)

• 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 544.3 if the Preparation Course has no effect.
• No. The probability indicates that is is possible by chance alone to randomly select a group of students with a mean as high as 544.3 if the Preparation Course has no effect.

Answer 1