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(MATH144)[2003](f)midterm~4660^_63885.pdf
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MATH 244 (L1) Applied Statistics

Mid-Term Examination October 24, 2003

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 4 questions in this exam. 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. 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.

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!!!





















P. T. O.
1. (25 marks) The following histogram shows the IQ scores of 250 gifted students. The mean and standard deviation are 165.3 and 14.1 respectively.














(a)
Briefly describe the distribution of the above IQ scores.
(3 marks)





(b)
Find the five number summary and hence sketch the boxplot for these IQ scores.
(10 marks)





(c)
Find the 95th percentile of the IQ scores of these 250 gifted students.
(5 marks)





(d)
Approximate the proportion of gifted students with IQ scores within one standard deviation from the mean.
(7 marks)















2. (25 marks) The number of times that an individual contracts a cold in a given year is a Poisson random variable with parameter . Suppose a new wonder drug (based on large quantities of vitamin C) has just been marketed that reduces the Poisson parameter permanently to for 75 percent of the population. For the other 25 percent of the population the drug has no appreciable effect on colds.



(a)
What is the chance that an individual who tried the drug will contract 2 colds in one year?
(5 marks)





(b)
Fifty individuals who tried the drug were sampled independently. Let X be the number of individuals in the sample who will contract 2 colds in one year. Find the mean and variance of X.
(6 marks)





(c)
A man tried the drug for last year and had 2 colds in that time. What is the probability that the drug was beneficial for him?
(6 marks)





(d)
What is the probability that the man in part (c) will contract less than 5 colds in the coming year?
(8 marks)




3. (25 marks) Suppose the length of life of ce