Question

Height is a normally distributed human characteristic. In the United States, men's heights have mean 69.1 inches and standard deviation 2.9 inches, while female's heights have mean 63.7 inches and standard deviation 2.7 inches.

Collect height data on a sample of n=3 men and n=3 women.

Complete the following for the sample of men and women separately:

1. List the raw data.
2. Transform each score into a standardized z-score.
3. Identify the percentile rank for each individual. Percentile rank is the percentage of scores in its frequency distribution that are equal to or lower than it. Thus, if someone is in the 90^th percentile for height, they are taller than 90% of the population.

Answer 1

assume data for Men (69,71,75)

for women - (63,64,62)

z-score = (X - mean)/sd

Men		Women
	z-score		z-score
69	-0.03448	63	-0.25926
71	0.655172	64	0.111111
75	2.034483	62	-0.62963

percetile = normsdist(z) in excel

Men
	z-score	percentile
69	-0.03448	0.4862
71	0.655172	0.7438
75	2.034483	0.9790
Women
	z-score	percentile
63	-0.25926	0.3977
64	0.111111	0.5442
62	-0.62963	0.2645