课程名称︰统计学上 课程性质︰必修 课程教师︰关秉宗 开课学院：生农院 开课系所︰森林系 考试日期（年月日）︰101/11/8 考试时限（分钟）：180 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 1. A box contains 1000 light bulbs. The probability that there is at least one defective item in the bos is 0.1, and the probability of having at least 2 defective bulbs is 0.05. Please find the probability for the following events. A. The box has no defective light bulb.(5%) B. The box has exactly 1 defective bulb.(5%) C. The box has at most 1 defective light bulb.(5%) 2. The blood type distribution among whites in the US is roughly as follows: A:40%, B:11%, AB:4%, and O:45%. If a white male is randomly selected to be typed, what is the probabilities that he will have a blood type of A, B or AB? 3. It is believed that 30% of the people that suffers from diabetes in a population are obese. The obesity rate in that population is about 35%, whereas the diabetic rate is about 25%. Please determine that if a person is randomly selected from that population, what is the probability that the person will not be obese, given that the person is not diabetic?(10%) 4. Let X~H(0,1), please calculate the following probabilities(20%) ↑很像草写H的符号 A.P(X≦0.0) B.P(X≦0.95) C.P(X≦1.5) D.P(X≦2.25) E.P(X≦3.0) F.P(X≦-1.5) G.P(X≧0.0) H.P(X≧2.5) I.P(X≧-3.0) J.P(-1.5≦X≦1.5) 5. Let X~H(5,16), please calculate the following probabilities(20%) ↑很像草写H的符号 A.P(X≦5.0) B.P(X≦8.8) C.P(X≦11.0) D.P(X≦14) E.P(X≦17.0) F.P(X≦-1.0) G.P(X≧0.0) H.P(X≧15) I.P(X≧-7.0) J.P(-1.0≦X≦11.0) 6. Life tables show the average numbers of survivors at various ages per 100000 live births. Age 20 45 65 Males 97108 92191 71385 Females 98040 95662 84483 If we assume that mortality rates are constant through time, we can use these numbers to estimate survial probabilities. Foe example, the probability of that a newborn boy live to age 65 is 0.71385, and a male ages 45 lives to age 65 is about 71385/92191. Please use these data to find the probabilities of A. a woman aged 20 will live to age 65(5%) B. a man and a woman will both live to age65(5%) C. a person aged 45 is male(5%) D. a person aged 45 will live to age 65(10%) Note: assume that 525 of the live births are males and 45% are females. 7. Extra credit problem Based on the binomial theorem, please show that the sum of a binomial distribution probability density funtion is 1. --

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