Statistics question?

Question

A particular group of men have heights with a mean of 171 cm and a standard deviation of 8 cm. Carl had a height of 174cm.?

.a. What is the positive difference between Carl's height and the mean?

b. How many standard deviations is that [the difference found in part (a)]?
.
c. Convert Carl height to a z score.

.d. If we consider "usual" heights to be those that convert to z scores between minus−2 and 2, is Carl's height usual or unusual?

Answer 1

a)  |Carl's height - mean|, where Carl's height = 174 cm, mean = 171 cm and | | is the absolute value

 

b)  Divide answer in a) by the standard deviation (8 cm)

 

c)  z = answer from (b)

 

d)  Is z between -2 and 2?