ps3sol_F08

# ps3sol_F08 - The Hong Kong University of Science and...

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The Hong Kong University of Science and Technology IS O M 111 - Business statistics ( Prof Inchi HU ) Problem Sheet 3 Suggested Solutions 1. (a) μ = 19.3 or \$19300 σ = 5.0309 or \$5030.9 (b) 0.0281 2. (a) 0.1056 (b) 13.42 (c) 0.9561 3. (a) Let x be the score of a student. So, x ~ N (65, ). Let c be the cut-off score for A. 2 10 45 . 81 c 645 . 1 10 65 c 05 . 0 ) 10 65 c Pr( 05 . 0 ) c Pr( = = = = z x where z is a standard normal random variable . (b) Let y be the no. of students getting Ds among the 5 chosen students. Then y ~ Bin(5,0.1). 4095 . 0 ) 9 . 0 ( 1 ) 0 Pr( 1 ) 1 Pr( 5 = = = = y y (c) Let a be the no. of student getting As among thee 100 chosen students. Then a ~ Bin(100,0.05). ) ) 95 . 0 )( 05 . 0 ( 100 ) 05 . 0 ( 100 5 . 8 Pr( ) 9 Pr( ) 8 Pr( = > z a a 0537 . 0 4463 . 0 5 . 0 ) 61 . 1 Pr( = = = z (d) 0062 . 0 ) 5 . 2 Pr( ) 10 65 40 Pr( ) 40 Pr( = < = < = < z z x Let f be the number of students failed among the 80 chosen students. Then

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## This note was uploaded on 09/18/2010 for the course BBA ISOM111 taught by Professor Hu during the Fall '08 term at HKUST.

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ps3sol_F08 - The Hong Kong University of Science and...

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