Height of a man

Question

The heights of adult men in America are normally distributed, with a mean of 69.1 inches and a standard deviation of 2.63 inches. The heights of adult women in America are also normally distributed, but with a mean of 64.5 inches and a standard deviation of 2.56 inches.

a) If a man is 6 feet 3 inches tall, what is his z-score (to two decimal places)?

z = 

b) If a woman is 5 feet 11 inches tall, what is her z-score (to two decimal places)?

z = 

c) Who is relatively taller?

1. The 5 foot 11 inch American woman
2. The 6 foot 3 inch American man

Answer 1

Remember, when calculating z scores we calculate for populations, not means. (also sometimes proportions)

Formula for Z = (x_µi - µ)/σ

A) For a person of the population of those who are of the biological male persuasion, with a mu of 69.1INCHES and a sigma of 2.63 INCHES, a Z score can be calculated for a 6ft 3 inch person as

Z_score = (75" - 69.1")/2.63"

B) A) For a person of the population of those who are of the biological female persuasion, with a mu of 64.5 inches and a standard deviation of 2.56 inches, a Z score can be calculated for a 5 ft 11 inch person from this population as

Z_score = (71" - 64.5")/2.56"

C) if we define relative as the probability of being higher (or lower) , the height which is more rare would be higher, relatively, the the height which is not so rare (assuming we are testing for P(z>Z_score) One does not have to calculate the actual probability, only note that a higher Zscore is more rare than a lower Z score (when looking at greater than average heights or positive Z scores.

So grasshopper, you have done the Z scores, which is larger?

remember. The population means and standard deviations are taken from population samples where the elements of the population are defined, in this case un modified biological men and women. This is only the distribution of the numerical populations. Separate populations for people gender identifying outside these populations either by choice or physical modification belong to separate populations with their own mean and standard deviation in height. The selection of a biological gender population to allow medical determinations does not in any way make any determinations on relative worths of any of the sub populations among one another.