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Practice exam 2

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David Wright

Final Exam ADM2303 STATISTICS FOR MANAGEMENT I December 17, 2007, 7.00-10.00pm Gym DEF Professors: Khoroshilov, Phansalker, Wright Time allowed: 3 hours. Closed book exam First Name .......................................................... Last Name .......................................................... Student Number ................................................. Signature ............................................................ Students can obtain full marks (50) by answering questions 1 – 5 Bonus marks (7.5) are available from questions 6 - 8 All questions are to be answered on the answer sheet in the space given. The back of the question paper should be used for rough work only. 1 Qu. #1. A telecommunications equipment vendor produces two lines of products (i) private network equipment and (ii) public network equipment. It estimates the market size for these two product lines in one year’s time as shown in the table: Estimated Market Size: $bn Mean Standard Deviation Private Network 7.6 1.2 Equipment Public network 4.3 0.5 Equipment (3) (a) Assuming that the markets for the two lines of products are independent of each other, calculate the mean and standard deviation of the estimated total market size in one year’s time. (4) (b) In fact, the correlation between the two markets is 0.47. (I.e. correlation coefficient = 0.47). Calculate the mean and standard deviation of the estimated total market size in one year’s time. (3) (c) The Vice President of the Private Network Equipment Division wants to be at least 87.5% sure of having enough capacity to meet estimated market size next year. We do not know the shape of the distribution of market size but we do know that the distribution is symmetric. What market size figure in $bn should the Vice President plan for, so as to be at least 87.5% sure the actual market will be lower than this figure? Qu. #2. A large survey of customers who called a customer service toll-free telephone number found that 46% of customers were satisfied with the service they received. Since the survey, the customer service agents have received additional training. After the training, interviews with 10 randomly selected customers found that 6 of them were satisfied with the service they received. (3) (a) What is the probability that 6 out of 10 randomly selected customers would have said they were satisfied with the service they received, before the training. (5) (b) What is the probability that 60 or more out of 100 randomly selected customers would have said they were satisfied with the service they received, before the training. (Hint: Use continuity correction.) (2) (c ) Do you think the training has improved customer satisfaction. State your reasons in two short sentences. Qu. #3. Gasprom and United Energy System (UES) are the two largest energy (oil, gas, and electricity) companies in Russia. The annual return on Gasprom shares is normally distributed with mean of 15% and a standard deviation of 25%. Return on the UES shares is also normally distributed. However, since the UES has higher debt-equity ratio, its shares have a higher expected return of 20% and a higher standard deviation of 35%. For simplicity, assume that stock returns are independent. (2) (a) What is the probability that you will get a positive return on any money invested in Gasprom for one year? (5) (b) Find the probability that the annual return % on Gasprom shares will exceed the annual return % on the UES shares. (3) (c) Anatoly Chubais, the CEO of the UES, claims that there is a 30% chance that next year the return on the UES shares will be more than R%. Find R. 2 Qu. #4. An unnamed government official claims that a Canadian taxpayer between 19 and 65 year old should expect to pay on average $20K ($20,000) in federal taxes in 2007 tax year. Assume that federal tax liabilities for Canadians are normally distributed (6) (a) You have concerns about his/her estimates of the average tax liability – you think it should be higher than $20K. You have randomly selected 10 people and computed their federal tax liabilities as follows: $28K $29K $27K $28K $25K $35K $24K $28K $19K $38K Does this data indicate that the official’s estimation of the mean is too low? State your reason clearly. (Hint: you may want to find a probability that any sample of size 10 will result in a sample mean that is equal to or higher than the sample mean of your sample.) (3) (b) What is the probability that the average tax payment of a randomly selected group of 60 taxpayers is less than $18K if the standard deviation of the federal tax payments of 19-65 year old Canadian taxpayers is $8K. (1) (c) What will be the effect on your answer to question (b) if the federal tax liabilities were not normally distributed? State your reason clearly. Qu. #5 (10 Marks) A power-drink manufacturer fills large 750 mL bottles with the power-drink. To test if the filling process is under control or not, the quality control department took 12 samples of 5 observations each and recorded the actual amount of drink in the bottles. Chart#1 is the resulting Xbar Chart based on the range, ‘R’ and Chart#3 is the resulting Xbar Chart based on the standard deviation, ‘s’. The Table Values of Control Chart Constants are given at the end of this Question. When asked, the UCL and LCL values must be calculated by using appropriate values from this table. Chart#1: X­Bar Chart based on R 1 751.5 UCL= 751.364 751.0 a M _ l 750.5 _ m
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