2003-Fall-Midterm - More PastPaper:...

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Unformatted text preview: More PastPaper: http://ihome.ust.hk/~cs_gxx ISMT111 Business Statistics Mid-Term Examination 17th October 2003 Directions 1) Answer ALL SIX questions. Marks are shown in square brackets. 2) There are 4 pages in this examination paper. Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing. 3) Key formulas and statistical tables are provided separately. 4) Calculator may be used in this examination. ht tp :// ih om e. us t.h k/ ~c s_ gx x/ 5) You are given TWO HOURS to complete this examination. Do not begin until you are told to do so. 1 More PastPaper: http://ihome.ust.hk/~cs_gxx Question 1: [16 Marks] The following table gives the revenue change (in percentage) of 10 companies in 2002: 3.4 -4.8 2.1 4.3 13.8 1.5 -2.4 -5.7 1.1 -0.6 (a) What are the sample mean, standard deviation and interquartile range of the revenue change? (b) Is there any extreme value in the sample? (c) Suggest and calculate a suitable location measure for the revenue change. Explain your answer. (d) Suppose we have another sample of five revenue changes whose mean and standard deviation are 1.2 and 4.78 respectively. Calculate the combined standard deviation of the fifteen observations. Question 2: [18 Marks] A company receives a shipment of twenty items. Because inspection of each individual item is expensive, it has a policy of checking a random sample of six items for such a shipment, accepting delivery if no more than one sampled item is defective. Suppose there are five defective items in a specific shipment and the random sample is chosen without replacements from that shipment. (a) What is the expected number of defective items in the sample? (b) What is the probability that the specific shipment is accepted? (c) Suppose the first item of the sample was found to be defective. What is the probability that the specific shipment is accepted? ht tp :// ih om e. us t.h k/ ~c s_ gx x/ (d) Suppose there is one defective item in the first four items of the sample. What is the probability that the specific shipment is accepted? 2 More PastPaper: http://ihome.ust.hk/~cs_gxx Question 3: [16 Marks] A record store owner assesses customers entering the store as high school age, university age, or older, and finds 30%, 50%, and 20% respectively of all customers fall into these categories. The owner also found that purchases were made by 20% of high school age customers, by 60% of college age customers, and by 80% of older customers. (a) What is the probability that a randomly chosen customer entering the store will make a purchase? (b) If a randomly chosen customer makes a purchase, what is the probability that this customer is high school age? (c) If a randomly chosen customer DOES NOT make a purchase, what is the probability that this customer is NOT high school age? Question 4: [14 Marks] Jerry, owner of Jerry’ Pizza, has a difficult decision on his hands. He has found that the s number of his famous “Jerry’ Supreme” pizzas that he sells has the following s probability distribution: Number of pizzas demanded (#) Probability 1 0.4 2 0.3 3 0.3 Since the preparation time for each pizza is lengthy, Jerry prepares all of the “Jerry’ s Supreme” pizzas in advance and stores them in the refrigerator. Because the ingredients go bad within one day, Jerry always throws out any unsold pizzas at the end of each evening. The cost of preparing each pizza is $70, and Jerry sells each one for $120. In addition to the usual costs, Jerry also calculated that each “Jerry’ Supreme” pizza that s is ordered but he cannot deliver due to insufficient stock costs him $40 in future business. (a) What is the probability distribution of Jerry’ profit from selling “Jerry’ s s Supreme” pizzas if he prepares 3 in advance? (b) What is Jerry’ expected profit from selling “Jerry’ Supreme” if he prepares 3 in s s advance? ht tp :// ih om e. us t.h k/ ~c s_ gx x/ (c) How many “Jerry’ Supreme” pizzas should Jerry stock each night in order to s maximize his expected profit? 3 More PastPaper: http://ihome.ust.hk/~cs_gxx Question 5: [16 Marks] The amount of time necessary to travel to Japan from Hong Kong is assumed to be a normal distribution with mean 5 hours and a standard deviation of 0.25 hour. (a) What is the probability that it will take between 4.5 and 5 hours? (b) Give the range of values symmetric about the mean such that the probability that the travel time is within that range is 80%. Question 6: [20 Marks] Suppose the lifetime of the florescent lamp is approximately normally distributed. Two brands of florescent lamps are under consideration. Brand A has mean 1700 hours and standard deviation 400 hours, whereas Brand B has mean 1600 hours and standard deviation 250 hours. (a) If the selection criterion is higher probability to last more than 1500 hours, which brand should be chosen? (b) Suppose that Brand A was chosen. The replacement policy is bulk replacement. The burned out lamps will not be replaced individually and instead at certain point of time the management will replace all lamps (burn out or not) by new ones to save labor cost. Assume that it is desirable to replace all lamps such that no more than 10% of them burn out. How long after the installation of new lamps should the bulk replacement take place? (c) Consider five lamps of brand A, what is the probability that exactly one will burn out before 2000 hours in use? (d) If 70% of the lamps are of brand A, 30% of the lamps are of brand B. What is the proportion of lamps will burn out before 2000 hours in use? ht tp :// ih om e. us t.h k/ ~c s_ gx x/ (e) Continue from (d). A lamp burns out before 2000 hours in use, what is the probability that it is of brand A? 4 ...
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