Question

1. A successful basketball player has a height of 6 feet 7inches or 201cm. Based on statistics from a data set, his height converts to the z score of

3.743.74.

How many standard deviations is his height above the mean?

2. If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: minus? 2.00, minus? 1.00, 0, 1.00, 2.00? Why?

A.

The z score of 0 is most preferable because it corresponds to a test score equal to the mean.

B.

The z score of

minus?2.00

is most preferable because it is 2.00 standard deviations below the mean and would correspond to the highest of the five different possible test scores.

C.

The z score of

minus?1.00

is most preferable because it is 1.00 standard deviation below the mean and would correspond to an above average test score.

D.

The z score of 1.00 is most preferable because it is 1.00 standard deviation above the mean and would correspond to an above average test score.

E.

The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores

3. Waiting times (in minutes) of customers at a bank where all customers enter a single waiting line and a bank where customers wait in individual lines at three different teller windows are listed below. Find the coefficient of variation for each of the two sets of data, then compare the variation.

Bank A (Line 1) Bank B (Line 2)

6.5 4.1

6.5 5.5

6.8 5.8

6.9 6.2

7.1 6.7

7.3 7.6

7.5 7.6

7.7 8.5

7.8 9.3

7.8 9.7

The coefficient of variation for the waiting times at Bank A is what %.

(Round to one decimal place as needed.)

The coefficient of variation for the waiting times at the Bank B is

what %.

(Round to one decimal place as needed.)

Is there a difference in variation between the two datasets?

4.

Answer 1

Question 1

The z-score is a measure how many standard deviations above (positive z-value) or below (negative z-value) the mean an observation is.

Now, the given z-score of the height of the basketball player is 3.74, thus we can conclude that the height of the basketball player is 3.74 standard deviations above the mean. [ANSWER]

Question 2

The correct option is E. The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores. [ANSWER]

Explanation:

Out of the given z-scores of -2, -1, 0, 1, 2, the highest positive z-score is 2 and we know that the z-score is a measure how many standard deviations above (positive z-value) or below (negative z-value) the mean an observation is.

Thus, if we would want to have highest marks in the exam then we would prefer a z-score of 2 and the correct option is E.

Options A, B, C and D are incorrect because they are all less than the 2, which is the highest z-value and thus gives the maximum possible test score whereas the z-values of -2, -1, 0 and 1 do not give the highest test scores.

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