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(MATH144)[2004](f)midterm1~4660^_10866.pdf
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MATH 244 Applied Statistics


Mid-Term Test I September 30, 2004




Please read the following instructions carefully before you begin the exam.


1. Do not begin until you are told to do so.

2. Please place your student identity card on your desk for verification purposes.

3. There are 5 questions in this test. You have to answer all questions. Please write down all your answers in your answer book. Show all your works.



4. You will have 1 hour and 30 minutes to complete the exam.

5. No books, notes or other reading materials are permitted. Some formulae that you may need are provided on the back of this page.

6. If you feel you need to think a lot for a question, skip it and return to it later. Some of the easiest question for you might be at the very end. So, choose your own order of answering the questions.

7. Anyone who is caught cheating, helping someone cheat, or who is suspected of cheating, will receive zero mark on this exam. There will be no exception.

8. Do your best, and good luck!!!














1. (30 marks) After a survey on the monthly salaries of 20000 college graduates, the following histogram was created.



(a)
Which measurement scale does the variable salary belong to?
(2 marks)





(b)
Briefly describe the distribution of the monthly salaries.
(3 marks)





(c)
Find the five number summary and hence sketch a box-plot. (Outlier detection is not need.)
(10 marks)





(d)
Approximate the mean monthly salary of these college graduates. How many of these college graduates have monthly salary above this mean?
(6 marks)





(e)
Is the mean monthly salary in (d) a suitable measure of central tendency for all the monthly salaries in this data set? Explain briefly.
(4 marks)





(f)
Suppose one of these college graduates, Thomas, told you that he has monthly salary not lower than $10000. How likely is that he has monthly salary less than $20000?
(5 marks)



2. (15 marks) State the definitions of

(a)
Mutually exclusive events;
(5 marks)





(b)
Independent events;
(5 marks)





(c)
Random variable.
(5 marks)



P. T. O.
3. (15 marks) From a group of 9 women and 7 men a committee consisting of 4 men and 4 women is to be formed. How many different committees are possible if

(a)
2 of the men refuse to serve together;
(5 marks)





(b)
2 of the women refuse to serve together;
(5 marks)





(c)
1 man and 1 woman refuse to serve together?
(5 marks)




4. (25 marks) A small plane has gone down, and the search is organized into three regions. Starting with the likeliest, they are :

Region
Initial Chance Plane is There
Chance of Being
Overlooked in the Search

Mountains
0.5