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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 5.3 5.3 million cells per microliter and a standard deviation of 0.3 0.3 million cells per microliter. ​(a) What is the minimum red blood cell count that can be in the top 23 23​% of​ counts? ​(b) What is the maximum red blood cell count that can be in the bottom 12 12​% of​ counts?

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Answer:

5.5217

4.9475

Step-by-step explanation:

Given that :

Mean (m) = 5.3

Standard deviation (s) = 0.3

Score

Minimum redbloodcell in top 23% count

Z = (x - m) / s

Z at 0.23 = 0.739

P(z> x) = 0.23 ; Z = 0.739

0.739 = (x - 5.3) / 0.3

0.739 * 0.3 = x - 5.3

0.2217 = x - 5.3

x = 0.2217 + 5.3

x = 5.5217

(b) What is the maximum red blood cell count that can be in the bottom 12​% of​ counts?

Z = (x - m) / s

P(z< x) = 0.12 ; Z = - 1.175 ( Z probability

-1.175 = (x - 5.3) / 0.3

-1.175 * 0.3 = x - 5.3

- 0.3525 = x - 5.3

x = - 0.352 + 5.3

x = 4.9475

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