Question

Suppose that people's heights (in centimeters) are normally distributed, with a mean of 165 and a standard deviation of 6. We find the heights of 60 people.
(a) How many would you expect to be between 157 and 173 cm tall?

Answer 1

(a)
Calculate the z-values of 157 and 173:
Z(157)=(157-165)/6=-4/3
Z(173)=(173-165)/6=4/3
Look up normal distribution table/calculator to find the difference
p=P(Z<173)-P(Z<157)
where p is the probability of finding people in this height range.
Multiply p by the number in the sample to get the expected value.