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 0.4 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 11 %of counts?

Answer 1

Answer:

(a) The minimum red blood cell count that can be in the top 21% of counts is 6.1.

(b) The maximum red blood cell count that can be in the bottom 11% of counts is 5.3.

Step-by-step explanation:

The random variable X can be defined as the number of red blood cells in adult males.

The random variable X can be approximated by a normal​ distribution.

The mean number of red blood cells is, μ = 5.8 million cells per micro liter.

The standard deviation of red blood cells is, σ = 0.4 million cells per micro liter.

(a)

Compute the value of x such that P (X > x) = 0.21 as follows:

   P (X > x) = 0.21

⇒ P (Z > z) = 0.21

The value of z is, 0.81.

*Use a z-table.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\0.81=\frac{x-5.8}{0.4}\\x=5.8+(0.4\times 0.81)\\x=6.124\\\approx6.1$

Thus, the minimum red blood cell count that can be in the top 21% of counts is 6.1.

(b)

Compute the value of x such that P (X < x) = 0.11 as follows:

   P (X < x) = 0.11

⇒ P (Z < z) = 0.11

The value of z is, -1.23.

*Use a z-table.

Compute the value of x as follows:

$z=\frac{x-\mu}{\sigma}\\-1.23=\frac{x-5.8}{0.4}\\x=5.8-(0.4\times 1.23)\\x=5.308\\\approx5.3$

Thus, the maximum red blood cell count that can be in the bottom 11% of counts is 5.3.