hw4sol - The Hong Kong University of Science and Technology...

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Page 1 of 3 The Hong Kong University of Science and Technology IS O M 111 - Business statistics Lecture Section (Prof Inchi HU) Assignment 4 Solution (Problem Sheet 3: #2, #3, #5 & #6) Solutions 2. (a) Let x be life of a nickel-cadmium battery x ~ N ( 20, 4 2 ) P ( x <15) = P( 4 20 15 < z ) = P( z < -1.25) = 0.5 – P(0 < z < 1.25) = 0.1056 (b) Let h be the number of hours of use the warranty should cover so that 5% of the batteries have to be replaced. P( x < h) = 0.05 P( 4 20 h < z ) = 0.05 P( 4 h 20 0 < < z ) = 0.45 4 h 20 = 1.645 h = 13.42 (c) x – number of defectives in the sample x ~ Bin(8, 0.1056) P( x 2) = p(0) + p(1) + p(2) = 8 0 C 0.8944 8 + 8 1 C 0.8944 1056 . 0 7 + 2 6 8 2 1056 . 0 8994 . 0 C = 2 6 7 8 1056 . 0 8994 . 0 28 1056 . 0 8994 . 0 8 8994 . 0 + +
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Page 2 of 3 3. (a) Let x be the score of a student. So, x ~ N (65, 2 10 ). Let c be the cut-off score for A. 45
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hw4sol - The Hong Kong University of Science and Technology...

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