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5) The blood cell counts (in million cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.4 million cells per microliter and a standard deviation of 0.4 million cells per microliter.

5) The blood cell counts (in million cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.4 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 25% of counts? b) what is the maximum red blood cell count that can be in the bottom 15% counts? c) The random variable x is normally distributed with mean μ = 18 and standard deviation σ 7.6 i If P(x >a) 0.40, find a If P(x 〈 a) = 0.60, find a

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Solution-1: Population means μ-5.4 Population standard deviation-σ-: 0.4 Part-A: Value of z-score, such that area under the normal curve to the right of it equal to 25%, is given by: z 0674 x 5.4 0.6740.4 x 5.670 Hence, minimum red blood cell count that can be in the top 25% of the counts-5.670 million cells per microliter Part-B Value of z-score, such that area under the normal curve to the left of it equal to 15%, is given by: Z-_ 1.036 -1.036-x-5.4 1036 0.4 4.985 Hence, maximum red blood cell count that can be in the bottom 15% counts-4.985 million cells per microliter Part-C: Population mean u 18 Population standard deviation-σ-: 7.6

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