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0301_ass3_sem2_2010_20110

# 0301_ass3_sem2_2010_20110 - THE UNIVERSITY OF HONG KONG...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 0301 Elementary Statistical Methods Assignment 3 (No need to hand in. Do all in preparation for the class test 9/3/2011.) *1. 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 equals 450 points? (ii) his total score exceeds 450 points? (ii) his average score exceeds 60 points? 2. 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 probability that (i) her total marks will exceed 280? (ii) her average marks will exceed 60? 3. David’s monthly income and expenditure are both normally distributed. They perform independently, with means and s.d.’s as follows: Parameter Income Expenditure Mean ( μ i ) \$8500 \$7300 S.D. ( σ i ) \$550 \$850 (a) What is the probability the he will be in red next month?

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