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?

Using the normal distribution, we have that the blood counts are:

a) 6.12 million cells per microliter.

b) 4.81 million cells per microliter.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

In this problem:

Item a:

This is the 100 - 21 = 79th percentile, which is X when Z has a p-value of 0.79, so X when Z = 0.807.

Hence, 6.12 million cells per microliter.

Item b:

This is the 11th percentile, which is X when Z has a p-value of 0.11, so X when Z = -1.227.

Hence, 4.81 million cells per microliter.

A similar problem is given at link

(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:

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:

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

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

step-by-step explanation: