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**

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