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 5.4 million cells per microliter and a standard deviation of0.3 million cells per microliter.

​(a) What is the minimum red blood cell count that can be in the top 22​% of​ counts?

​(b) What is the maximum red blood cell count that can be in the bottom10​%

of​ counts?

Answer 1

solution

Using standard normal table,

P(Z > z) = 22%

= 1 - P(Z < z) = 0.22

= P(Z < z ) = 1 - 0.22.

= P(Z < z ) = 0.78

= P(Z < 0.77) = 0.78  

z =0.77 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 0.77*0.3+5.4

x= 5.631

(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+5.4  

x= 5.784