hw11_sol - IEOR 172: Probability and Risk Analysis for...

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Unformatted text preview: IEOR 172: Probability and Risk Analysis for Engineers, Fall 2007 Homework 11 Solution Chapter 8 Question 2 (a) P { X 85 } E[ X ] / 85 = 15 / 17 (b) P { 65 X 85 } = 1- P {| X- 75 | > 10 } 1- 25 / 100 (c) P {| n i =1 X i /n- 75 | > 5 } 25 25 n so need n = 10. Question 4 (a) P { 20 i =1 X i > 15 } 20 / 15 (b) P ( 20 X i =1 X i > 15 ) = P ( 20 X i =1 X i > 15 . 5 ) P ( Z > 15 . 5- 20 20 ) = P { Z >- 1 . 006 } . 8424 Question 13 (a) P { X > 80 } = P n X- 74 14 / 5 > 15 / 7 o P { Z > 2 . 14 } . 0162 (b) P { Y > 80 } = P n Y- 74 14 / 8 > 24 / 7 o P { Z > 3 . 43 } . 0003 (c) Using that SD ( Y- X ) = q 196 / 64 + 196 / 25 3 . 30 we have P { Y- X > 2 . 2 } = P { ( Y- X ) / 3 . 3 > 2 . 2 / 3 . 3 } P { Z > . 67 } . 2514 . (d) same as in (c) Question 18 Let Y i denote the additional number of fish that need to be caught to obtain a new type when there are at present i distinct types. Then Y i is geometric with paramter...
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hw11_sol - IEOR 172: Probability and Risk Analysis for...

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