Answered: the red blood cell counts (in millions…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 31PPS

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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 28% of counts? (b) what is the maximum red blood cell count that can be in the bottom 14% of counts? (a) the minimum red blood cell count is nothing million cells per microliter."

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

Expert Solution

Step 1

Given:

$μ = 5.8 σ = 0.4$

a) The minimum red blood cell count that can be in the top 28% of counts is obtained as below:

$\begin{array}{rcl} P (X > x) & = & 0.28 \\ P (\frac{X - μ}{σ} > \frac{X - 5.8}{0.4}) & = & 0.28 \\ P (Z > \frac{X - 5.8}{0.4}) & = & 0.28 \\ 1 - P (Z < \frac{X - 5.8}{0.4}) & = & 0.28 \\ P (Z < \frac{X - 5.8}{0.4}) & = & 0.72 \end{array}$

The p-value is obtained from excel using "=NORMSINV(probability)".

Output obtained using Excel is given below:

From the output, the value is 0.5828.

$\begin{array}{rcl} \frac{X - 5.8}{0.4} & = & 0.5828 \\ X & = & (0.5828 \times 0.4) + 5.8 \\ = & 0.23312 + 5.8 \\ = & 6.03312 \end{array}$

Thus, the minimum red blood cell count that can be in the top 28% of counts is 6.03 million cells per microliter.

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