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(MATH144)[2002](f)midterm~4660^_69677.pdf
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MATH 244 Applied Statistics

Mid-Term Examination October 25, 2002


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 6 questions in this exam. You have to answer all the questions.

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

5. Show all your works on all questions.

6. You are allowed to use a formula sheet (A4 size written on both sides). No books, notes or other reading materials are permitted. Statistics tables that you may need are provided below.

7. 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.

8. 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.

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











1. (20 marks) The following graph shows the U.S. household income data.



(a)
Comment on and critique the above graph.
(8 marks)

(b)
Is the distribution of the numbers of children symmetric, positively skewed, or negatively skewed? Why?
(3 marks)

(c)
Find the median household income.
(4 marks)

(d)
Find the inter-quartile range of the household incomes.
(5 marks)




2. (10 marks)
(a)
If we toss a fair coin 10 times independently, what is the probability that there are exactly 5 heads and 5 tails?
(4 marks)

(b)
If we toss a fair coin 1000 times independently, what is the probability that there are exactly 500 heads and 500 tails?
(6 marks)






3. (20 marks) For each of the following random variables X, write down the distribution and the values of the parameters (e.g. b, , , etc.) that best models X. If the distribution does not belong to any named family, write down its pmf (or pdf).




(a)
Customers arrive at an automated teller machine independently and at random. During lunch hour, customers arrive at the machine at a rate of one per minute on average. X is the number of people who arrive between 12:15pm and 12:30pm.
(4 marks)

(b)
Calls to an Internet service provider are placed independently and at random. During evening hours, the service provider receives an average of 100 calls an hour. X is the waiting time (in minutes) between consecutive calls tonight.
(4 marks)

(c)
Roll two fair six-faces-dice independently. X is the sum of the numbers showing on the two dice.
(4 marks)

(d)
The average height of men at a certain city is 67 inches, and the standard deviation is 2 inches. X is the average height of a sample of 50 men randomly selected from this city, with replacement.
(4 marks)

(e)
A