Question

1.) A successful basketball player has a height of 6 feet 6 inches, or 198 cm. Based on statistics from a data set, his height converts to the z score of 3.38.

How many standard deviations is his height above the mean?

The player's height is [ans1] standard deviation (s) 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: − 2.00, − 1.00,  0, 1.00,  2.00? Why?

a. 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.

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

c. The z score of -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.

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

e. 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.

3.) For a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 39 beats per minute, the mean of the listed pulse rates is 72.0 beats per minute, and their standard deviation is 11.2 beats per minute.

a.) What is the difference between the pulse rate of 39 beats per minute and the mean pulse rate of the females? The difference is ____  beats per minute.

b.) How many standard deviations is the difference found in part  (a)? The difference is ____ standard deviations.

c.) Convert the pulse rate of 39 beats per minutes to a z score. The z score is ____.

d.) If we consider data speeds that convert to z scores between −2 and 2 to be neither significantly low nor significantly  high, is the pulse rate of 39
beats per minute significant? The lowest pulse rate is ____.

Answer 1

1) The player's height is 3.38 standard deviations above the mean.

2) Option - a) The z-score of 2 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) a) The difference is 72 - 39 = 33

b) 33/11.2 = 2.95
The difference is 2.95 standard deviations.

c) The z-score = (X - )/

                        = (39 - 72)/11.2

                        = -2.95

d) Since the z-score for the pulse rate of 39 is less than -2, so it is significant.

z = -2

or, (X - )/ = -2

or, (X - 72)/11.2 = -2

or, X = -2 * 11.2 + 72

or, X = 49.6

The lowest pulse rate is 49.6 .