Question

Heights of men and women in the U.S. are normally distributed. Recent information shows:

Adult men heights:    µ = 69.6 inches with σ = 3 inches.

Adult women heights: µ = 64.1 inches with σ = 2.7 inches.

3.

The middle 60% of U.S. women will be between ___ inches and ___ inches tall

(round to the whole inch)

What percent of U.S. men are 6 ft. or shorter:

(round to the 2nd decimal place)

If a man is selected at random from the U.S. population, what is the probability that he is between 66 and 71 inches tall?

(round to the 4th decimal place)

Answer 1

(3)

= 64.1

= 2.7

Middle 60%corresponds to area = 0.60/2 = 0.30 on either side of mid value.

Table of Area Under Standard Normal Curve gives Z = 0.84

Low side:
Z = - 0.84 = (X - 64.1)/2.7

So,

X = 64.1 - (0.84 X2.7)

= 64.1 - 2.268

=61.832

High side:
Z = 0.84 = (X - 64.1)/2.7

So,

X = 64.1 + (0.84 X2.7)

= 64.1 + 2.268

=66.368

So,

Answer is:

(62, 66)

(4)

= 69.6'

= 3

To find P(X72):

Z = (72 - 69.6)/3 = 0.80

Table gives area = 0.2881

So,

P(X72) = 0.5 + 0.2881= 0.7881

So,

Answer is:

0.79

(5)

To find P(66 < X < 71):

Case 1: From 66 to mid value:
Z = (66 - 69.6)/3 = - 1.10

Table gives area = 0.3643

Case 2: From mid value to 71:
Z = (71 - 69.6)/3 = 0.47

Table gives area = 0.1808

So,

P(66<X<71) = 0.3643 + 0.1808 = 0.0.5451

So,

Answer is:

0.5451