hw9_418_10 - 20. X B (100, 0.65), Y B (65, 22.75) Y 5 65 a)...

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20. X B (100 , 0 . 65) , Y B (65 , 22 . 75) a) p ( X > = 50) p ( Y > 49 . 5) p ( Y - 65 22 . 75 > 49 . 5 - 65 22 . 75 ) = 1 - p ( Z < = - 3 . 25) = 1 - Φ( - 3 . 25) = 0 . 9994 . b) p (60 < = X < = 70) = p (59 . 5 < Y < 70 . 5) p ( 59 . 5 - 65 22 . 75 < Y - 65 22 . 75 < 70 . 5 - 65 22 . 75 ) = p ( - 1 . 15 < Z < = 1 . 15) = Φ(1 . 15) - Φ( - 1 . 15) = 0 . 7498 . c) p ( X < = 74) p ( Y < 74 . 5) p ( Y - 65 22 . 75 < 74 . 5 - 65 22 . 75 ) = p ( Z < 1 . 99) = 0 . 9767 , 24. let X denotes the lifetime of interactive compute chips. X N (1 . 4 * 10 6 , (3 * 10 5 ) 2 ), then p ( X < 1 . 8 * 10 6 ) p ( X - 1 . 4 * 10 6 3 * 10 5 < 1 . 8 * 10 6 - 1 . 4 * 10 6 3 * 10 5 ) = p ( Z < = 1 . 33) = 0 . 9082 . let Y denotes the number of chips whose lifetime is less than 1 . 8 * 10 6 , then Y B(100,0.9082). p ( Y > = 20) p ( X - 90 . 82 8 . 337 < 19 . 5 - 90 . 82 8 . 337 ) = Φ(24 . 7) = 1 . 28.
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hw9_418_10 - 20. X B (100, 0.65), Y B (65, 22.75) Y 5 65 a)...

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