Question

A standardized test for graduate school admission has a mean score of 151 with a standard deviation of 8 and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of 4 students at a time. A larger organization teaches classes of 25 at a time. Both organizations publish the mean scores of all their classes.

1.) What would you expect the sampling distribution of mean class scores to be for each organization?

A.) The distributions cannot be determined, since the Central Limit Theorem does not apply

B.) Both distributions will be approximately normal with a mean of 151

C.) The distribution for the larger organization will be approximately normal with a mean of 151. The sample size for the larger organization is too small for the Central Limit Theorem to apply

D.) The distribution for the smaller organization will be approximately normal with a mean of 151. The sample size for the larger organization is too large for the Central Limit Theorem to apply

2.) If either organization has a graduating class with a mean score of 159, they’ll taks ouf a full-page ad in the local school paper to advertise. Which organization is more likely to have that success? Explain by filling in the blanks.

A mean score of 159 is ___ SD above the mean for the smaller organization, and ____ SD above the mean for the larger organization. It is more likely that the _____ organization will have that success.

3.) Both organizations advertise that if any class has an average score below 147, they’ll pay for everyone to retake the test. Which organization is at a greater risk to have to pay? Explain by filling in the blanks below.

A mean score of 147 is ____SD below the mena for the smaller organization, and ____SD below the mean for the larger organizatkon. The ____ organization is at greater risk to have to pay.

Answer 1