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

5.6

million cells per microliter and a standard deviation of

0.5

million cells per microliter.​(a) What is the minimum red blood cell count that can be in the top

21​%

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

10​%

of​ counts?

​

Answer 1

Solution :

Given that ,

mean = = 5.6

standard deviation = = 0.5

a)

The z - distribution of the 21% is,

P( Z > z ) = 21 %

1 - P( Z < z ) = 0.21

P( Z <  ) = 1 - 0.21

P( Z < z ) = 0.79

P( Z < 0.806 ) = 0.79

z = 0.806

Using z - score formula,

X = z * +

= 0.806 * 0.5 + 5.6  

= 6.003

b)

The z - distribution of the 10 % is,

P( Z < z ) = 10%

P( Z < z ) = 0.10

P( Z < -1.282 ) = 0.10

z = -1.282

Using z - score formula,

X = z * +

= -1.282 * 0.5 + 5.6  

= 4.96