Question

7. As part of a research study you measure participants' heights in inches. The average height of all participants is 70 inches, and the standard deviation is 3 inches. One of your participants, Rachel, who is 65 inches tall, wants to know what percentage of the participants are taller than she is. What is the answer to her question?

Answer 1

95% of the fellow students of this girl are taller than she is

Explanation:

First find the z-score for the value 65 when the mean is 70 and the standard deviation is 3:

65 - 70

z = --------------- = -5/3, or approximately z = -1.667.

3

Next we determine what fraction of these heights lie above z = -1.667. This can be done on a calculator that has built-in statistical functions, or a table of z-scores. Using the TI-83 Plus: the area above z = -1.667 is 0.95.

In conclusion, 95% of the fellow students of this girl are taller than she is.