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59. Cholesterol Suppose that the blood cholesterol level of all men aged 20 to 34 follows the Normal distribution with mean μ-188 milligrams per deciliter (mg/dl) and standard deviation σ 41 mg/dl. (a) Choose an SRS of 100 men from this population Describe the sampling distribution of . (b) Find the probability that x estimates μ within +3 mg/dl. (This is the probability that i takes a value between 185 and 191 mg/dl.) Choose an SRS of 1000 men from this population. Now what is the i rol)ability that x talls within ::3 mg/dl offa? In what sense is the larger sample better? (c)
math   Statistics-And-Probability   
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Answer #1

a)

p cn smple a i.e. 1,-188 The SD of sampling distribution of sample mean 12. σ--SDK SD Sqrt(n) 41/ 100 4.1

b)

b)P185 <x <191)=P 185-188 191-188 41A00 <2<41/マ100 P(-0.7317 <Z <0.7317) P(Z <0.73171)- P(Z <-0.7317) 0.76783-0.23218 0.53565 Since Area under the standard normal table c)P(185 <x < 191)=P 185-188 41N1000 2-41. A000 191-188 P(-2.31386 <Z <2.31386) = P(Z < 2.31386)-P(Z <-2.31386) 0.98966-0.01034-0.97932 Since Area under the standard normal table

The probability in part (C) is larger than that of Part (B) Therefore, the large sample is better

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