Question

The red blood cell counts​ (in millions of cells per​ microliter) for a population of adult males can be approximated by a normal​ distribution, with a mean of 5.2 million cells per microliter and a standard deviation of 0.4 million cells per microliter. ​(a) What is the minimum red blood cell count that can be in the top 28​% of​ counts? ​(b) What is the maximum red blood cell count that can be in the bottom 16​% of​ counts? ​(a) The minimum red blood cell count is ____ million cells per microliter. ​(Round to two decimal places as​ needed.)

Answer 1

P(X < A) = P(Z < (A - mean)/standard deviation)

Mean = 5.2 million cells per microliter

Standard deviation = 0.4 million cells per microliter

a) Let the minimum red blood cell count that can be in top 28% be T

P(X > T) = 0.28

P(X < T) = 1 - 0.28 = 0.72

P(Z < (T - 5.2)/0.4) = 0.72

(T - 5.2)/0.4 = 0.58

T = 5.432 million cells per microliter

b) Let the maximum red blood count that can be in the bottom 16% be B

P(X < B) = 0.16

P(Z < (B - 5.2)/0.4) = 0.16

(B - 5.2)/0.4 = -0.99

B = 4.804 million cells per microliter