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 0.3 million cells per microliter.

​(a) What is the minimum red blood cell count that can be in the top 20​% of​ counts?

​(b) What is the maximum red blood cell count that can be in the bottom 10​% of​ counts?

​(a) The minimum red blood cell count is _____ million cells per microliter.

​(Round to two decimal places as​ needed.)

Answer 1

solution

Using standard normal table,

P(Z > z) = 20%

= 1 - P(Z < z) = 0.20

= P(Z < z ) = 1 - 0.20

= P(Z < z ) = 0.80

= P(Z < 0.84 ) = 0.80

z = 0.84 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x=0.84 *0.3+5.8

x= 6.052

(B)Using standard normal table,

P(Z < z) = 10%

= P(Z < z) = 0.10  

= P(Z <-1.28 ) = 0.10

z = -1.28 Using standard normal z table,

Using z-score formula  

x= z * +

x= -1.28 *0.3+5.8

x= 5.416