ma316f03hw13

ma316f03hw13 - MA 316: MATHEMATICAL PROBABILITY ASSIGNMENT...

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Unformatted text preview: MA 316: MATHEMATICAL PROBABILITY ASSIGNMENT #13 SOLUTIONS: SECTIONS 6.2 and 6.3 (OPTIONAL) FALL 2003 6.14: If the observed value of X is 81.2 from a random sample of size n = 20 from N ( , 80), then a 95% confidence interval for is X- 1 . 96 n , X + 1 . 96 n = 81 . 2- 1 . 96 80 20 , 81 . 2 + 1 . 96 80 20 ! = (77 . 28 , 85 . 12) . 6.15: If X is the mean of a random sample of size n from a distribution that has mean and variance 2 = 10, then a 90% confidence interval for is X- 1 . 645 n , X + 1 . 645 n . Therefore if P ( X- 1 < < X + 1) = 0 . 90 then we must have 1 = 1 . 645 3 n . Solving for n gives n = 24 . 35 so let n = 25 . 6.16: If a random sample of size n = 17 from a normal distribution N ( , 2 ) yields x = 4 . 7 and s 2 = 5 . 76, we need to find a 90 percent confidence interval for . Since we dont know or 2 we must use that the random variable T = X- S/...
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ma316f03hw13 - MA 316: MATHEMATICAL PROBABILITY ASSIGNMENT...

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