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Assignment 3 - 0910 THE UNIVERSITY OF HONG KONG DEPARTMENT...

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0910 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 0301 Elementary Statistical Methods Assignment 3 (Problems for self-practice.) 1. The following frequency table is given: Class 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 – 79 Total f i 7 9 14 12 9 8 6 65 Find mean ( μ ), standard deviation ( σ ), variance ( σ 2 ), median, mode, coefficient of variation, and skewness. 2. Alan participates in an athletics competition. The game consists of 5 items. Alan’s performance in each item follows a normal distribution with mean and s.d. (both in points) as follows: Item ( i ) 1 2 3 4 5 Mean ( μ i ) 85 90 80 93 78 S.D. ( σ i ) 4 3 5 2 6 If Alan’s performances are independent from game to game, what is the probability that (i) his total score exceeds 450 points? (ii) his average score exceeds 60 points? 3. An examination consists of 4 papers. Betty’s performance in each paper has a normal distribution with mean and s.d. (both in marks) as follows: Paper ( i ) 1 2 3 4 Mean ( μ i ) 70 58 75 55 S.D. ( σ i ) 3 7 4 5 If Betty’s performances are independent from paper to paper, what is the proba- bility that (i) her total marks will exceed 280? (ii) her average marks will exceed 60?
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S&AS: STAT 0301 Elementary Statistical Methods 2 4. David’s monthly income and expenditure are both normally distributed.
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