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(ISOM111)[2007](f)midterm~2546^_10368.pdf
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ISMT111 Business Statistics
Midterm Examination
For sections 5 & 6 only
18 October 2007
Directions
1) Answer ALL FIVE questions. Marks are shown in square brackets.
2) There are 4 pages in this examination paper, which includes a normal table. Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing.
3) Key formulas are provided separately.
4) Calculator may be used in this examination.
5) You are given TWO HOURS to complete this examination. Do not begin until you are told to do so.
Question 1: [15 Marks]
The stem-and-leaf displays of scores for two groups of students taking the same examination from a statistic course is given below.
(a)
Please describe the shape of the score distribution for Group I.
(b)
Although the mean of Group II 74.0 is lower than 75.29 for Group I, after checking other descriptive statistics, the instructor of the statistics course concluded that Group II did better in the examination. Please give as many reasons as possible to support the instructors conclusion.
0 0 0
1 1
2 2
3 3
4 5 4
5 46 5
6 78 6 124
7 4566 7 1337
8 002456 8 01126
9 48 9 0115
Group I Group II
Question 2: [20 Marks]
Junk mails are unsolicited bulk e-mail messages sent indiscriminately by advertisers. They cause low productivity and fraud. An internet service provider developed a junk mail filter. A junk e-mail message will be stopped by the filter with probability 0.9. Those e-mail messages stopped by the filter will be moved to a folder for further inspection. A non-junk message will pass through the filter with probability 0.95. For a particular customer of the internet service provider, 30% of e-mail messages are junk.
(a)
What are the prior probabilities in this problem?
(b)
What is the percentage of e-mail messages stopped by the filter?
(c)
If an e-mail message is stopped by the filter, whats the probability it actually is a junk mail?
(d)
In (b) & (c) which one is the posterior probability and which one is the empirical probability? Please explain briefly.
Question 3: [15 Marks]
There are two technology development projects A, B. If pursue separately, A, B will cost 0.5 million and 0.7 million, respectively. The project manager estimated that probabilities of success for A and B are 0.7 and 0.5, respectively. If successful, the profit from A, B will be 2 million and 2.5 million, respectively. There will be no profit, if fail. The net profit equals profit minus cost.
(a)
What is the meaning of the probabilities in this problem? (classical probability? subjective probability? or long run relative frequency of occurrence?) Please explain briefly.
(b)
Please calculate the total expected net profit from projects A and B.
(c)
Please calculate the variance of net profit for B.
Question 4: [25 Marks]
A tennis player plays on t