Chapter 8 - Pg 427 Question #2 a) P{X 85} E[X] / 85 = 15/17...

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Unformatted text preview: Pg 427 Question #2 a) P{X 85} E[X] / 85 = 15/17 0.8824 b) P{65 X 85} = 1 P{ | X 75 | > 10} 1 25/100 = c) P{ =- n i i n X 1 75 > 5} 25/25n So we need n = 10 to ensure with probability @ least 0.9 that the class average would be within 5 of 75. 1 Pg 427 Question #3 Let Z be a distributed N(0,1). So, P{ =- n i i n X 1 75 > 5} P{ | Z | > n 0.5 } 0.1 So we need n = 3 in this case. 2 3 Pg 427 Question #5 Let X i denote the i th roundoff error. So E = 50 1 i i X = 0 and Var = 50 1 i i X = 50. Since we have a uniform distribution, Var(X 1 ) = 50/12 since 0.5+X ~ Uniform(0,1). So, we can see that Var(X) = Var(1/2 + X) = 1/12. Thus it is clear: P{ = n i i X 1 > 3} P { | N(0,1) | > 3(12/50) 0.5 } using the C.L.T. = 2P{N(0,1) > 1.47} = 0.1416. 4 Pg 427 Question #6 Let X i denote the outcome of the i th role then E[X i ] = 3.5 and Var[X i ] = 35/12 and thus P{...
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This homework help was uploaded on 04/01/2008 for the course MATH 425 taught by Professor Buckingham during the Winter '08 term at University of Michigan.

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Chapter 8 - Pg 427 Question #2 a) P{X 85} E[X] / 85 = 15/17...

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