The distribution of hemoglobin in grams per deciliter of blood if approximately N(14,1) in women and approximately 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?B) What percent of men have less hemoglobin than the women's mean hemoglobin?C) What percent of men have more hemoglobin than the women's mean hemoglobin?

Question
Asked May 5, 2019

The distribution of hemoglobin in grams per deciliter of blood if approximately N(14,1) in women and approximately 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?

B) What percent of men have less hemoglobin than the women's mean hemoglobin?

C) What percent of men have more hemoglobin than the women's mean hemoglobin?

check_circleExpert Solution
Step 1

Given the distribution of haemoglobin in grams per deciliter of blood in women is normally distributed with mean 14 and standard deviation 1 and n men it is normally distributed with mean 16 and standard deviation 1.

Let X - represent distribution of womens haemoglodin and Y- represent men's haemoglobin distributions respectively.

The percentage of women have haemoglobin than the men's mean haemoglobin is                 P( X > 16).

We find the Z score for X = 16 using the below shown Z score formula and write P( X > 16) as P( Z > 2).

With reference to the Z table shared below the probability that Z score is greater than 2 is 0.0228.

P(Z > 2) = P(X>16) = 0.0228 

The proportion of women who have more haemoglobin than men's mean is 0.0228. So converting it inot percentages we say 2.28% of women have more haemoglobin than men's mean haemoglobin level.

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Step 2

The percentage of men having less haemoglobin than women\'s haemoglobin is calculated by  P(Y  < 14) where Y~N(16,1).

We find the Z score here using the below mentioned formula and write P( Y < 14) =                P( Z < -2).

Using the Z distribution table ...

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