# 94ffx - STATISTICS FOR MANAGEMENT I Dec 9 1994...

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1 STATISTICS FOR MANAGEMENT I Dec. 9, 1994 1900-2200 (corrected version) NAME: S.N. Section: Time: 3 hours INSTRUCTIONS: ALL ANSWERS (INCLUDING BRIEF EXPLANATIONS) GO ON THE LEGAL-SIZED ANSWER SHEET. THIS EXAM QUESTION BOOKLET WILL NOT BE MARKED. However, space is provided here for your rough work. These booklets must be deposited in the box provided. Calculators and 1 sheet of notes provided. Q 1. [4] The welds on tin cans must be done correctly to avoid the possibility of food becoming contaminated later. Despite a lot of care, about 1 in 8,000 cans is defective. The bean canning line at H J Heinz receives a shipment of 10 gross of cans (1 gross = 144 = 12 dozen). What is the probability two cans are defective in the shipment. Q 2. [6] Tinton is a small industrial town with 4000 houses. For a typical day, the average electrical power requirement of a house is 800 watts with standard deviation 200 watts. There are also 100 institutional (i.e., government, school or industrial) sites. These require an average of 16000 watts of power with standard deviation of 4000 watts. Tinton Hydro has a peak supply capacity of 4.9 Megawatts. If demand exceeds supply, there will be a brownout or else a complete power cut. If houses use more power in the evening while institutions use power more during the day, then demand between them will be negatively correlated. Suppose the correlation is in fact -0.4. What is now the probability of a brownout or blackout.

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2 Q 3. [3] A street person accosts people to ask for "loose change". Naturally he hopes to get a Loony, but only 10% of accostees actually give him one. On average, how many people must he accost before he gets a Loony? Q 4. The following output comes from an analysis of file sizes in bytes in three directories on a computer. (Real data!) This information is often important for optimizing the performance of disk management software. Below we present some numerical and graphical summaries of this data. MTB > desc c1-c3 N MEAN MEDIAN TRMEAN STDEV SEMEAN cfg 94 7763 208 3719 20809 2146 gmk 17 58795 13147 50802 81030 19653 nis 115 17603 5511 11950 35417 3303 MIN MAX Q1 Q3 cfg 3 117001 40 1702 gmk 54 237443 654 103923 nis 207 302728 2645 18974 MTB > let c12=log(c2) MTB > note log is NATURAL (base e) logarithm = ln MTB > name c12 'ln_gmk' MTB > stem c12 Stem-and-leaf of ln_gmk N = 17 Leaf Unit = 0.10 1 3 9 1 4 2 5 7 6 6 3448 6 7 8 8 23 (1) 9 4 8 10 06 6 11 146 3 12 023 a) [2] Compute the interquartile range for the files in the directory "cfg". b) [2] Compute the coefficient of variation for files in the directory "nis". c) [2] Compute the 40th percentile of the log of the length of files in the directory "gmk". d) [1] From your answer in (c), what is the 40th percentile of the length of files in the directory "gmk"? e) [2] Using the descriptive statistics, what set of file sizes has the greatest dispersion?
3 Q 5. [4] Electric space heaters often use nichrome wire heating elements. The elements made by Keep-U-Warm have undergone extensive testing and been found to have a lifetime that is exponentially distributed with mean lifetime of 1600 hours. What is the probability a new element will last at least 1000 hours?

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4 Q 6. Identify the most likely probability distribution (along with its parameters) which
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