課程名稱︰統計學
課程性質︰必修
課程教師︰陳郁蕙
開課學院：管理學院
開課系所︰會計系
考試日期（年月日）︰2006/11/28
考試時限（分鐘）：120分鐘
是否需發放獎勵金：是，謝謝。
（如未明確表示，則不予發放）
試題 :
1.已知某著名大學中共有450名教授，其中100名為女性教師，160名是社會科
學院的老師。而100名女性老師中，又有40名任教於社會科學院。今隨機抽
取一名老師，定義事件A為抽到女性老師，事件B為抽到社會科學院的老師。
請說明A和B這兩個事件是否為獨立事件？是否為互斥事件？（10分）
2.參加校慶活動的學生中，大一、大二、大三、大四的學生各佔四分之一，其
中大一學生中的百分之三十五，大二學生中的百分之二十五，大三學生中的
百分之二十，大四學生中的百分之十五為女生。如今隨機抽出一名學生參加
校長餐會。如果抽出的為女學生，則其為大一學生的機率為何？其為大三學
生的機率為何？（10分）
3.若X為一隨機變數，E(X)=10，且P({X小於等於7})=0.2，P({X大於等於13})
=0.3。則X的變異數至少為何？（10分）
4.If a real estate office sells 1.6 houses on an average weekday and
sales of houses on weekdays are Poisson distributed,
what is the probability of selling exactly four houses in one day?
What is the probability of selling no houses in one day?
What is the probability of selling more than five houses in a day?
What is the probability of selling 10 or more houses in a day?
What is the probability of selling exactly four houses in two days?
（20分）
5.Purchasing magazine reported the results of a survey in which buyers
were asked a series of questions with regard to Internet usage. One
question asked was how they would use the Internet if security and
other issues could be resolved. Seventy-eight percent said they would
use it for pricing information, 75% said they would use it to send
purchase orders, and 70% said they would use it for purchase order
acknowledgements. Assume that these percentages hold true for all
buyers. A resercher randomly samples 20 buyers and asks them how they
would use the Internet if security and other issues could be resolved.
（15分）
a.What is the probability that exactly 14 of these buyers would use the
Internet for pricing information?
b.What is the probability that all of the buyers would use the Internet
to send purchase orders?
c.What is the probability that fewer than 12 would use the Internet for
purchase order acknowledgements?
6.The Zimmerman Agency conducted a study for Residence Inn by Marriott of
business travelers who take trips of five nights or more. According to
this study, 37% of these travelers enjoy sightseeing more than any other
activity that they do not get to do as much at home. Suppose 120 randomly
selected business travelers who take trips of five nights or more are
contacted. What is the probability that fewer than 40 enjoy sightseeing
more than any other activity that they do not get to do as much at home?
（13分）
7.The exponential distribution can be used to solve Poisson-type problems
in which the intervals are not time. The Air Travel Consumer Report
published by the U.S. Department of Transportation reported that in recent
year, America West led the nation in fewest occurrences of mishandled
baggage, with a mean rate of 3.39 per 1000 passengers. Assume mishandled
baggage occurrences are Poisson distributed. Using the exponential
distribution to analyze this problem, determine the average number of
passengers between occurrences. Suppose baggage has just been mishandled.
What is the probability that at least 500 passengers will have their
baggage handled properly before the next mishsndled occurs? What is the
probability that the number will be fewer than 200 passengers?（12分）
8.某無線電視台八點檔『天下第N味』的製作人調查發現該節目平均收視率為8.5%，
標準差為0.94%。又已知全台灣約有1000萬人會收看電視節目，且收視率服從一常
態分配。而該電視台老闆就讀EMBA時統計學報告需要電視台當紅節目之收視人數的
中位數、四分位距（Q1,Q2,Q3）、第95百分位數等資料。問製作人會提供給老闆的
數據為何？（10分）
9.某工廠有甲乙兩條生產線，其產品的良率分別為X、Y，皆服從常態分配
N(85%,(5%)^2)，且這兩條生產線是相互獨立。求甲生產線良率優於乙生產線良率
且兩條生產線的良率皆大於80%之機率。（10分）
Hint 1：若隨機變數X和Y獨立，則由隨機變數X產生的事件會和隨機變數Y所產生的
事件獨立。
Hint 2：若對甲乙兩條生產線作相同的限制，則甲生產線優於乙生產線的機率與乙
生產線優於甲生產線的機率相等。
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※ 編輯: elwoodchen 來自: 140.112.243.22 (01/21 18:53)