Question

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? Round to two decimal places. A. ​82.26% B. ​4.09% C. ​17.69% D. ​16.11%

Answer 1

For normal distribution, P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 4.577 million cells per microliter

Standard deviation = 0.382 million cells per microliter

P(women have red blood cell counts in the normal range from 4.2 to 5.4 million cells per​ microliter) = P(X < 5.4) - P(X < 4.2)

= P(Z < (5.4 - 4.577)/0.382) - P(Z < (4.2 - 4.577)/0.382)

= P(Z < 2.154) - P(Z < -0.987)

= 0.9844 - 0.1618

= 0.8226

= 82.26%