Question

Suppose the heights of adult women follow a normal distribution with a mean of 65.5 inches and a standard deviation of 2.75 inches. Determine the following:

1.) What percent of adult women are taller than 6 feet (72 inches)?

2.) What percent of adult women are taller than 5 feet (60 inches)?

3.) What percent of adult women are between 60 and 72 inches tall?

4.) Because of the high cost of materials, the company has decided that they cannot make pants in all sizes. Determine the heights that correspond to

a.) The bottom 8% of the population

b.) The upper 6% of the population

Answer 1

(there are more than 4 parts, as per policy i am answering first 4 parts)

P(z<Z) table :

x : height in inches

1. percent of adult women are taller than 6 feet (72 inches)

P(x>=72) :

2. percent of adult women are taller than 5 feet (60 inches)

P(x>=60) :

3.

P(60<=x<=72) :

4.

a.

bottom 8% : P(z<Z) = 0.08

Z = -1.41

x = 65.5 + (-1.41)*2.75

= 61.6225

bottom 8% : height <= 61.6225 inches

b.

upper 8% : P(z<Z) = 1-0.08 = 0.92

Z = 1.41

x = 65.5 + (1.41)*2.75

= 69.3775

upper 8% : height >= 69.3775 inches

(please UPVOTE)