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hw5sol_F10

# hw5sol_F10 - The Hong Kong University of Science and...

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Unformatted text preview: The Hong Kong University of Science and Technology IS O M 111 - Business statistics Assignment 5 Solution (Problem Sheet 3: #1, #11 & #12) Solutions 1. (a) μ = E( x ) = 19.3 or \$19300 E( x 2 ) = 397.8 σ = 2 2 ) ( E μ − x = 5.0309 or \$5030.9 (b) x ~ N ( μ , σ 2 /n ) P( x > 20.5) = P( 8 / 0309 . 5 3 . 19 5 . 20 − > z ) = P( z > 1.91) = 0.5 – 0.4719 = 0.0281 11. (a) Let x be the monthly sales of Dark-Man Toothpaste. x ~ N (1000, 150 2 ) P( x > 1100) = P( z > 0.67) = 0.5 – 0.2486 = 0.2514 (b) Let c be the required stock for the monthly demand. Then P( x < c) = 0.95 P( z < 150 1000 c − ) = 0.95 P(0 < z < 150 1000 c − ) = 0.45 150 1000 c − = 1.645 c = 1246.75 (c) Let x i be the sales of the i th month in the next year, i = 1, 2, …, 12 P( ∑ = 12 1 i i x > 12600) = P( x > 1050) where x = ∑ = 12 1 12 1 i i x and is distributed as N (1000, 150 2 /12) Note: Large sam ple is not required because we are sam pling from a norm al population....
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hw5sol_F10 - The Hong Kong University of Science and...

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