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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 Nor-mal. 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
- Staff
- Economics, Normal Distribution, Standard Deviation, Brad, 1 dollar