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Question description

Consider the following situation, and answer each of the following multiple choice questions. In your write-up, just list the sub-question letter (A-J) and your answer – no need to restate the question or to justify your answer.

Situation: You have 400 data points, which are normally distributed with a mean of 90 and a standard deviation of 10. All scores are integers. Then one new data point is added, which is far above the top end of the distribution. (Thus, the new data point has the very highest score in the distribution, by a considerable margin.)

A. When the new data point is added, what happens to the sample size (N)?

B. When the new data point is added, what happens to the mean?

C. When the new data point is added, what happens to the value of the mode?

D. When the new data point is added, what happens to the number of modes in the distribution?

E. When the new data point is added, what happens to the range of the distribution?

F. Assuming the standard deviation of the old distribution was greater than 1, when the new data point is added, what happens to the value of the variance of the new distribution?

G. When the new data point is added, what happens to the value of the skewness of the distribution?

H. What happens to the value of the z score of the new mean calculated using the 401 data points, compared to the value of the z score of the old mean calculated using the original 400 data points?

I. What happens to the number of scores that are greater than 110?

J. What happens to the number of scores that are greater than 170?

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