課程名稱︰統計學上
課程性質︰必修
課程教師︰關秉宗
開課學院：生農院
開課系所︰森林系
考試日期（年月日）︰101/11/8
考試時限（分鐘）：180
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
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%)
↑很像草寫H的符號
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%)
↑很像草寫H的符號
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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