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 5.8 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 26​% of​ counts? ​(b) What is the maximum red blood cell count that can be in the bottom 13​% of​ counts?

Answer 1

Solution:-

Given that,

mean = = 5.8

standard deviation = = 0.4

a) Using standard normal table,

P(Z > z) = 26%

= 1 - P(Z < z) = 0.26  

= P(Z < z) = 1 - 0.26

= P(Z < z ) = 0.74

= P(Z < 0.64 ) = 0.74  

z = 0.64

Using z-score formula,

x = z * +

x = 0.64 * 0.4 + 5.8

x = 6.06

minimum red blood cell = 6.06

b) Using standard normal table,

P(Z < z) = 13%

= P(Z < z ) = 0.13

= P(Z < -1.13 ) = 0.13  

z = -1.13

Using z-score formula,

x = z * +

x = -1.13 * 0.4 + 5.8

x = 5.35

maximum red blood cell = 5.35