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# 2 - THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS...

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THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT 0302 Business Statistics Assignment 2 (Do all. Hand in solutions to the FOUR starred questions on or before 27.2.09.) *1. (a) Circular metal discs are manufactured in a factory in large quantities. The target diameter of the discs is 16.00 cm. It is known that this dimension follows a normal distribution with a standard deviation of 0.03 cm. An item is randomly drawn. Determine a 90% prediction interval for its diameter. (b) A large batch of electrical equipment has been produced. The quality in question is the resistance, which is normally distributed with a mean of 175 ohms and a standard deviation of 0.7 ohms. Any piece whose resistance lies between 170 and 180 ohms is considered to satisfy customer’s specifications. Determine the six- sigma process limits. How well does the producer’s quality satisfy the customer’s specifications? c) A lift has the following specifications “Capacity: 20 persons, Maximum load: 1250 kg”. It is known that the weights (including their personal belongings) of the passengers taking the lift have a normal distribution with a mean of 62.5 kg and a standard deviation of 8.5 kg. What is the probability that the lift will be overloaded when it is filled to capacity? (d) Two assembly parts, A and B , have N(8 . 45 , 0 . 03 2 ) and N(8 . 60 , 0 . 04 2 ) distributions (unit of measurement: cm), respectively. Assembly is random. It is specified that the clearance should lie between 0.08 and 0.20. Find the proportion of rejects due to too-tight or too-loose fittings. 2. (a) The length of a certain kind of item is distributed normally with mean 8.5 cm and standard deviation 0.02 cm. Any item whose length exceeds 8.565 cm must be scrapped. Find the proportion of scraps in a large batch of such items. (b) The lengths of the sardines received by a cannery have a normal distribution with mean 11.52 cm and standard deviation 0.5 cm. What percentage of all these sardines are: (i) shorter than 10.00 cm, (ii) from 10.50 to 12.00 cm long? (c) On a certain Bank of China 24-hour banking machine which keeps only \$100 bank notes, the demand for cash in any ordinary weekend has a normal distribution with mean \$135,000 and standard deviation \$15,000. If the bank wants to be at least 85% sure that enough \$100 bank notes are available to cope with clients’ demands, how much money must it keep in the machine just before 1:00 p.m. on Saturday?

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