A group of 894 women aged 70-79 had their height and weight measured. The mean height was 159 cm with a standard deviation of 5 cm and the mean weight was 65.9kg with a standard deviation of 12.7kg. Both sets of data are fairly normal.

Question

A.) Suppose you were asked for a range of typical heights and weights for this population of women. What values would you give? Explain.
B.) Which of the two measurements appears more variable? Explain.
C.) What percentage of the population is expected to be taller than 166cm?
D.) What percentage of the population is expected to weigh between 55 and 75kg?
E.) Above what weight will 85% of the population lie?

Answer 1

This applet will be very useful

http://davidmlane.com/normal.html

You don't even have to find the z-scores, just enter the data as given

Answer 2

A.) about 99% of a normally distributed population lies within 2½ standard deviations of the mean
159 cm ± (2½ * 5 cm)
65.9 kg ± (2½ * 12.7 kg)

B.) the weight seems more variable because the s.d. is a larger fraction of the mean

C.) 7 cm above the mean is 1.4 s.d.
this is about 8% of the population

D.) 55 is (10.9/12.7) s.d. below the mean, and 75 is (9.1/12.7) s.d. above

this is about 60% of the population

E.) this is slightly more than 1 s.d. below the mean
a weight of about 53 kg