Question

The distribution of hemoglobin in grams per deciliter of blood is approximately N(14,1)N(14,1) in women and approximately N(16,1)N(16,1) in men.

Use software or Table B to find the answers.

(a) What percent of women have more hemoglobin than the men's mean hemoglobin? Give your answer to two decimal places.

Percent of women:

%

(b) What percent of men have less hemoglobin than the women's mean hemoglobin? Give your answer to two decimal places.

Percent of men:

%

(c) What percent of men have more hemoglobin than the women's mean hemoglobin? Give your answer to two decimal places.

Percent of men:

%

Answer 1

Solution :

Given that ,

X N(14,1) ( women)

mean = = 14

standard deviation = = 1

X N(16,1) ( men)

mean = = 16

standard deviation = = 1

a) P(x > 16) = 1 - p( x< 16)

=1- p P[(x - ) / < (16 - 14) / 1 ]

=1- P(z < 2)

Using z table,

= 1 - 0.9772

= 0.0228

The percentage is = 2.28%

b) P(x < 14) = P[(x - ) / < (14 - 16) / 1]

= P(z < -2)

Using z table,

= 0.0228

The percentage is = 2.28%

c) P(x > 14) = 1 - p( x< 14)

=1- p P[(x - ) / < (14 - 16) / 1 ]

=1- P(z < -2)

Using z table,

= 1 - 0.0228

= 0.9772

The percentage is = 97.72%