Assignment 3 solutions

Assignment 3 solutions - THE UNIVERSITY OF HONG KONG...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 0302 Business Statistics Assignment 3 - solutions 1. The frequency distribution table: i Class Class mark i x Frequency i f 1 10 – 20 15 8 2 20 – 30 25 10 3 30 – 40 35 15 4 40 – 50 45 12 5 50 – 60 55 10 6 60 – 70 65 8 7 70 – 80 75 6 8 80 – 90 85 6 Total 75 Mean = 46.2 Standard deviation = 20.5887 Variance = = 423.8933 2 20.58867 Median = 75 33 2 40 10 12 = 43.75 Mode = 15 10 30 10 (15 10) (15 12) −+− =36.25 Coefficient of variation = 20.5887 46.2 = 0.4456 (44.56%) Skewness = 3(46.2 43.75) 20.5887 = 0.3570 (35.70%) 2. Given that Alan’s score in the i th item = ( ) 2 ~, ii XN i μσ , i =1,2,3,4,5. (i) Let T be Alan’s total score. By independence, T = 55 5 2 11 1 i i μ σ == = ⎛⎞ ⎜⎟ ⎝⎠ ∑∑ . i.e. . () ~ 450,90 TN 1
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() 475 450 475 90 2.64 0.0041 PT P Z PZ ⎛⎞ >=> ⎜⎟ ⎝⎠ => = (ii) Let A be Alan’s average score. Now, A = 55 5 2 2 11 1 ~, 5 ii i XN 1 i μ σ == = ∑∑ . i.e. . ~9 0 , 3 . 6 AN 85 90 85 3.6 2.64 0.9959 PA >= > = 3. Given that Betty’s score in the i th paper = ( ) 2 i μσ , i =1,2,3,4. (i) Let T be Betty’s total score. By independence, T = 44 4 2 1 i i = .
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This note was uploaded on 11/06/2009 for the course STAT STAT0302 taught by Professor Prof.chiu during the Spring '09 term at HKU.

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Assignment 3 solutions - THE UNIVERSITY OF HONG KONG...

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