Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per
Microliter. Approximately what percentage of women have red blood cell counts in the
Normal range from 4.2 to 5.4 million cells per microliter?

Question

Quizplus · Accepted Answer

To find the percentage of women with red blood cell counts in the normal range from 4.2 to 5.4 million cells per microliter, we use the properties of the normal distribution. First, we calculate the z-scores for the lower and upper limits of the range:- For 4.2 million cells/μL: $Z = \frac{4.2 - 4.577}{0.382} \approx -0.987$- For 5.4 million cells/μL: $Z = \frac{5.4 - 4.577}{0.382} \approx 2.151$Using standard normal distribution tables or a calculator, we find the probabilities corresponding to these z-scores:- The area to the left of $Z = -0.987$ is approximately 0.1619 (16.19%).- The area to the left of $Z = 2.151$ is approximately 0.9842 (98.42%).To find the percentage of women within this range, we subtract the lower percentage from the higher percentage: $98.42\% - 16.19\% = 82.23\%$.This calculation shows that approximately 82.31% of women have red blood cell counts within the normal range of 4.2 to 5.4 million cells per microliter, which corresponds to choice A.

Assume That the Red Blood Cell Counts of Women Are