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Unformatted text preview: 3) = . 31+ . 40 = . 71 , P ( ¯ X ≥ 3) = pnorm(3,2.88,.1487,lower.tail=F)=.2098 Problem 5.52 1. μ X =(500)(.001)=.50, σ X = √ 249 . 75 =15.8 2. In the long run Joe will make about 50 cents on any 1 dollar bet. 3. If ¯ X is Joe’s average pay off over a year then μ ¯ X = μ X = . 50 , ¯ X = σ X √ 104 =1.5497. The CLT says that ¯ X is approximately normal. 4. Use the normal approximation so P ( ¯ X ≥ 1) =pnorm(1,.50,1.5497,lower.tail=F)=0.3734828 Problem 5.60 1. The central limit theorem says that the sample means will be roughly Normal. Note that the distribution of individual scores cannot ahve extreme outliers because all the scores are between 1 and 7. 2. ¯ Y has mean 4.8 and standard deviation .2835 ¯ X has mean 2.4 and standard deviation .3024 3. ¯ Y¯ X is approximately normal with mean 2.4 and standard deviation .4145 4. P ( ¯ Y¯ X ) = pnorm(1,2.4,.4145,lower.tail=F)=0.9996 2...
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 Fall '08
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 Economics, Normal Distribution, Standard Deviation, Brad, 1 dollar

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