Question

The distribution of hemoglobin in grams per deciliter of blood is approximately N(14,1) in women and approximately N(16,1) in men.a. What percent of women have hemoglobin greater than 17 grams per deciliter?

Answer 1

Answer:

0.13%

Step-by-step explanation:

We dont care about the men distribution, so we can focus on women distribution of hemoglobin in grams per deciliter. Lets call Y the random variable that states the hemoglobin in grams per deciliter for a woman. The exercise tells us that Y has distribution N(14,1) We want Y greater than 17, so we need to calculate P(Y > 17). We can standarize Y by substracting its expected value 14 and by dividing by its standard deviation 1.

The variable $Z = \frac{Y - 14}{1} = Y-14$ is a Standard normal random variable, and its cummulated distribution function, Ф, is tabulated. The values of Ф can be found on the attached file.

P(Y > 17) = P(Y-14 > 17-14) = P(Z > 3) = 1 - P(Z ≤ 3) = 1 - Ф(3) = 1 - 0.9987 = 0.0013

Thus, the percent of women with greater hemoglobin than 17 grams per deciliter is 100*0.0013 = 0.13%