推 cy94 :太快了吧XDDDD 11/21 20:29
課程名稱︰統計學一上
課程性質︰
課程教師︰游孝元
開課學院：管理學院
開課系所︰國際企業學系
考試日期（年月日）︰2013/11/21
考試時限（分鐘）：14:20~17:00
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
一、(20%)Suppose the length of time (in hours) between emergency arrivals at
St. Williams Hospital is two hours.
Assume the length of time follows exponential distribution:
1. What is probability that an emergency arrival comes within one hour.
2. What is the probability that more than 4 hours pass without an
emergency arrival?
Assume the emergency arrivals follow Poisson distribution
3. Find the mean and standard deviation of emergency arrivals per hour.
4. What is the probability that no emergency arrivals comes within 4 hours?
二、(20%)We surveyed 12 NTU students to understand the intention of building a
new library. Suppose students agree or disagree to build a new library on
campus is 50-50. **2^12=4096**
1. What is the probability that exactly 6 students agree and 6 students
disagree to build a new library on campus?
2. What is the probability that more than nine persons disagree to build
the library?
3. Is it appropriate for us to use the normal distribution to approximate
the original binomial distribution? Why?
4. Use normal distribution to re-calculate the probability that more than
nine persons disagree to build the library.
三、(20%)Toss two fair dice and let x1 and x2 be the points of the first and
the second dice respectively. Define y=x1-x2
1. write down the sample space of variable y
2. define event A that variable y is nonnegative, find the probability of
event A.
3. calculate P(x1<x2∪A)、(x1>x2|A)
四、(30%)小筒油品公司生產食用油，每瓶標示950ml，大桐油品公司生產之食用油每瓶
標示960ml。另根據消基會統計，小筒與大桐食用油每瓶容量變異數分別為100ml^2、
400ml^2，假設兩者皆為常態分配，請問：
1. 隨機抽取一瓶小筒食用油，其容量不到935ml之機率為何？
2. 消費者今天買到一瓶容量達980ml之食用油，你認為較可能是哪個牌子？
3. 若消基會將針對油品容量標示不實進行裁罰(實際容量過少)，選定不實比率若高於
5%即裁罰，試問大桐公司該如何進行品管，以維護公司商譽？
五、(10%)蘋果電腦的iphone手機向來是3C科技界的熱門話題。蘋果是否該推出大螢幕尺
吋的 iphone 手機也常常在台灣熱門論壇網站 mobile01 有激烈討論。贊成者認為
大尺寸手機瀏覽方便，且為潮流趨勢，反對者認為3.5至4吋手機易於單手操作，且攜
帶方便。今假設台灣蘋果愛用者(網路上稱之為果粉)市占率為1/4，非果粉為3/4。針
對是否改推出大螢幕尺寸的 iphone 手機，果粉與非果粉表現兩樣情。果粉中認為該
推出大尺寸手機的比率僅為0.08，反觀非果粉陣營則有８成認為該推出大螢幕手機。
請問若隨機抽取一位支持蘋果推出大螢幕手機的使用者，其為果粉的機率為何？
另附有參考公式：
Binomial Hypergeometric Geometric Poisson Uniform Exponential Normal皆有
另附有常態分配表
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