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 5.9 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 23​% of​ counts? ​(b) What is the maximum red blood cell count that can be in the bottom 12​% of​ counts? ​ ​(Round to two decimal places as​ needed.)

Answer 1

Given that,

mean = = 5.9

standard deviation = =0.4

Using standard normal table,

P(Z > z) = 23%

= 1 - P(Z < z) = 0.23

= P(Z < z ) = 1 - 0.23

= P(Z < z ) = 0.77

= P(Z < 0.74) = 0.77  

z = 0.74 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 0.74*0.4+5.9

x= 6.196

x=6.20 rounded

b.

Using standard normal table,

P(Z < z) = 12%

= P(Z < z) = 0.12  

= P(Z < -1.18) = 0.12

z =-1.18 Using standard normal table,

Using z-score formula  

x= z * +

x= -1.18 *0.4+5.9

x= 5.43