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 5.1 million cells per microliter and a standard deviation of 0.3 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 13​% of​ counts??

Answer 1

Solution:-

Given that,

mean = = 5.1

standard deviation = = 0.3

Using standard normal table,

P(Z > z) = 28%

= 1 - P(Z < z) = 0.28  

= P(Z < z) = 1 - 0.28

= P(Z < z ) = 0.72

z =0.58

Using z-score formula,

x = z * +

x = 0.58 * 0.3+5.1

x = 5.274

B.

Using standard normal table,

P(Z < z) = 13%

= P(Z < z) = 0.13

= P(Z < -1.13) = 0.13

z = -1.13 Using standard normal table,

Using z-score formula  

x= z * +

x=-1.13 *0.3+5.1

x= 4.761