Question

This Question: 5 pts A particular group of men have heights with a mean of 176 cm and a standard deviation of 6 cm Richard had a height of 196 cm. a. b. c. What is the positive difference between Richard's height and the mean? How many standard deviations is that [the difference found in part (a)? Convert Richard's height to a z score. d. f we consider "usual heights to be those that convert to z scores between -2 and 2. is Richard's height usual or unusual? a. The positive difference between Richards height and the mean is cm b. The difference is standard deviations. (Type an integer or decimal rounded to two decimal places as needed) c. The z score is (Type an integer or decimal rounded to two decimal places as needed) d. Is Richard's height usual or unusual? O Usual O Unusual

Answer 1

Solution:

a. The positive difference between Richard's height and the mean is $\small \boldsymbol{20}$ cm.

Because the difference between Richard's hight and mean is $\small 196-176=20$

b. The difference is $\small \boldsymbol{3.33}$ standard deviations.

Because the 20 divided by 6 is 3.33

c. The z-score is $\small \boldsymbol{3.33}$

$\small z=\frac{196-176}{6}=3.33$

d. Is Richard's height usual or unusual?

Answer: Unusual

Because Richard's height is more than 2 standard deviations above the mean