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?

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Mathematics

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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?

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Answers (1)

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Dale Hernandez · 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

Step-by-step 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