Question

The distribution of red blood cell counts is different for men and women in a certain population. For​ both, the distribution is approximately Normal. For men the middle​ 95% range from 4.34 to 5.95 million cells per​ microliter, and for women the middle​ 95% have red blood cell counts between 3.53 and 4.64 million cells per microliter. Complete parts (a) and (b) below

a. What is the mean for the men? Explain your reasoning

b. What is the mean for women? Explain your reasoning

Answer 1

Solution:

Given: The distribution of red blood cell counts is different for men and women in a certain population and the distribution is approximately Normal for both.

Part a) What is the mean for the men? Explain your reasoning

For men the middle​ 95% range from 4.34 to 5.95 million cells per​ microliter.

Mean is the center or mid point of confidence interval or center value of middle 95% area is nothing but mean. Since Normal distribution is symmetric about the mean value.

Thus find mid point of given range.

Mid Point = ( Lower Limit + Upper Limit) / 2

Mid Point = ( 4.34 + 5.95) / 2

Mid Point = 10.29

Mid Point = 5.145

Thus mean for the men = 5.145 million cells per​ microliter.

Part b) What is the mean for women? Explain your reasoning

For women the middle​ 95% have red blood cell counts between 3.53 and 4.64 million cells per microliter.

Thus find mid point of range 3.53 to 4.64

Mid Point = ( Lower Limit + Upper Limit) / 2

Mid Point = ( 3.53 + 4.64 ) / 2

Mid Point = 8.17 / 2

Mid Point = 4.085 million cells per​ microliter.

Thus mean for the women = 4.085 million cells per​ microliter.