課程名稱︰統計學一上 課程性質︰必修 課程教師︰雷立芬 開課學院：管理學院 開課系所︰國企系 考試日期（年月日）︰2011/11/23 考試時限（分鐘）：190分 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 1. In a certain city, 35% of the families have a MasterCard, 22% have an American Express card, and 28% have a Visa card. Eight percent of the families have both a MasterCard and an American Express card. Twelve percent have both a Visa card and a MasterCard. Six percent have both an American Express card and a Visa card. a. What is the probability of selecting a family that has either a Visa card or an American Express card? b. If a family has a MasterCard, what is the probability that it has a Visa card? c. If a family, what is the probability that it has a MasterCard? d. Is possession of a Visa card independent of possession of a MasterCard? Explain it in detail. e. Is possession of an American Express card mutually exclusive of possession of a Visa card? Why or why not? 2. The bivariate distribution of X and Y is shown as follows: X Y 1 2 3 1 0.06 0.42 0.12 2 0.04 0.28 0.08 Determine the mean and standard deviation of 3X-2Y. 3. A small independent physicians' practice has three doctors. Dr. Sarabia sees 41% of the patients, Dr. Tran sees 32%, and Dr. Jackson sees the rest. Dr. Sarabia requests blood tests on 5% of her patients, Dr. Tran requests blood tests on 8% of his patients, and Dr. Jackson requests blood tests on 6% of her patients. An auditor randomly selects a patient from the past week and discovers that the patient had a blood test as a result of the physician visit. Whar is the probability that the patient saw Dr. Sarabia? 4. Analyst generally believe that random phone calls are Poisson distributed. Suppose phone calls to a switchboard arrive at an average rate of 2.4 calls per minute. a. If an operator can handle at most five calls per minute, what is the probability that the operator will be unable to handle the calls in any one- minute period? b. What is the probability that one or fewer calls will arrive in a 15-second period? c. What is the expected (average) amount of time between calls? d. What is the probability that aminute or more woulf elapse betweem incoming calls? 5. Assume that random variable X is normally distributed. The interval between 2.4 and 17.6 is symmetrically spread around mean. The probabiliry of the interval is 0.95. Please find the probability that X is less than 5.03. 6. A population consists of the following six values: 1, 3, 5, 7, 9 and 11. Assuming that you sample with replacement, list all sample of size 2, and derive the sampling distribution of the sample mean. 7. Direct marketing companies are turning to the Internet for new opportuni- ties. A recent study showed that 73% of all direct maketers conduct transac- tions on the Internet. Suppose a random sample of 300 direct marketing companies is taken. a. What is the probability that between 210 and 234 (inclusive) direct market- ing companies are turning to the Internet for new opportunities? b. What is the probability that 78% or more of direct marketing companies are turning to the Internet for new opportunities? --

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