Question

The average height of a 13 year old male in the U.S. is 60 inches, with a standard deviation of 2 inches. The average weight of a 13 year old male in the U.S. is 100 pounds, with a standard deviation of 5 pounds. If Daniel, a 13 year old male, is 68 inches tall and weighs 115 pounds, is his height or weight more unusual?

Answer 1

The larger the magnitude of the z-score in each case, the more unusual the situation is.

Height: mean 60, std. dev. 2. If Daniel is 68 inches tall, the z score describing his height is

68-60

z = ------------ = 4 Any z score whose magnitude is greater than 2 is very

2 unusual. In this case, Daniel's height is practically off

the scale!

Weight

______

115-100

z = ------------- = 3 This is considered to be very unusual, but not so

5 unusual as a z-score of 4 (above).

Answer 2

Since the average height is 60 inches and its deviation is 2 inches, one deviation to the right (or higher) is 62 inches (60 + 2). Two deviations is 64 inches, three deviations is 66 inches, and four deviations is 68 inches.

Since the average weight is 100 pounds and its deviation is 5 inches, we repeat the process from finding heights to get to 115 pounds. That takes three deviations.

The MORE deviations away, the more unusual it is. So the height (4 deviations) is more unusual than the weight (3 deviations).