Question

A particular group of men have heights with a mean of 181 cm and a standard deviation of 6 cm. Earl had a height of 196 cm. a. What is the positive difference between Earl​'s height and the​ mean? b. How many standard deviations is that​ [the difference found in part​ (a)]? c. Convert Earl​'s height to a z score. d. If we consider​ "usual" heights to be those that convert to z scores between minus2 and​ 2, is Earl​'s height usual or​ unusual?

Answer 1

a. 15

b. based on the result of part a, 15 standard deviation above the mean.

c. 2.5

d. Earl's height is unusual

Explanation:

We have that "x" would be the height of Earl = 196, the mean m = equals 181 and the standard deviation (sd) = 6, now:

a. the positive difference between the mean and Earl's height:

D = x - m

D = 196 - 181 = 15

b. based on the result of part a, 15 standard deviation above the mean.

c. The z value is given by:

z = x - m / sd

replacing:

z = (196 - 181) / 6

z = 2.5

d. the z-score is unusual since the value of z is 2.5 which is a value greater than than 2 standard deviations above the mean, which means that Earl's height is unusual