Question

17. Height of Men and Women in the U.S. Women: μ= 64 inches , σ = 3.5 Men: μ= 70 inches , σ = 4

a. calculate the z score that corresponds to a women height of 68 inches.

b. state the percentile ranking for that score.

c. for both women and men in the US, calculate the z score and raw score (in inches) that separates the tallest 2.5% from the 97.5% of scores below.  

d. for both women and men in the US, calculate the z score and raw score in inches, that separates the shortest 2.5% of the population from the other 97.5%

f. What percent of women and men in the US have heights between the two z scores you calculated to answer questions c and d ?

Answer 1

Women: μ= 64 inches , σ = 3.5

Men: μ= 70 inches , σ = 4

We know that,

.

a.

the z score that corresponds to a women height of 68 inches,

z = (68 - 64)/3.5

z = 1.1428.

b.

the percentile ranking for that score,

87.34

Therefore, the score represents,

87th percentile

c.

for both women and men in the US, the z score and raw score (in inches) that separates the tallest 2.5% from the 97.5% of scores below is,

The z score that separates the tallest 2.5% from the 97.5% is 1.96

The raw score for women is,

1.96 = (x - 64)/3.5

x = 70.86 inches

The raw score for men is,

1.96 = (x - 70)/4

x = 77.84 inches

d. for both women and men in the US, the z score and raw score in inches, that separates the shortest 2.5% of the population from the other 97.5% is,

The z score that separates the shortest 2.5% from the 97.5% is - 1.96

The raw score for women is,

-1.96 = (x - 64)/3.5

x = 57.14 inches

The raw score for men is,

-1.96 = (x - 70)/4

x = 62.16 inches

f.

The percent of women and men in the US have heights between the two z scores 1.96 and -1.96 is,

P(-1.96 < z < 1.96) = 95%