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(MATH244)midterm01F_L1.pdf
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Mid-term Examination
MATH 244 (L1) Applied Statistics
Mid-Term Examination October 29, 2001
Time allowed : 90 minutes

Answer all questions.
1. (25 marks) The following histogram shows the distribution of the amounts of time (in seconds) of 10000 jobs processed by a large mainframe computers central processing unit.

(a)
Is the distribution symmetric, positively skewed, or negatively skewed? (4 marks)

(b)
Construct the frequency distribution table for the CPU times. (6 marks)

(c)
Find the five number summary. (10 marks)

(d)
Sketch a box-plot for the CPU times. (5 marks)


2. (25 marks) In a flexible manufacturing system, let X be the number of machines available and Y be the number of sequential operations required to process a part. The joint distribution was tabulated below.
Y
X 0 1 2
1 0 0.05 0.1
2 0.15 0.1 0.15
3 0.3 0.15 0

(a)
Are X and Y independent? Why? (5 marks)

(b)
Find the correlation coefficient between X and Y . (12 marks)

(c)
Suppose it is known that there are at least two machines available. What (8 marks) is the probability that we need exactly one operation to process a part?


P. T. O.
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Mid-term Examination
3.
(10 marks) Computer jobs submitted to a computer system at a rate of one per five minutes in accordance with a Poisson process. Find the probability that there will be at least three jobs submitted to the system from 3:00pm to 3:30pm.

4.
(10 marks) A large freight elevator can transport a maximum of 10,000 pounds (5 tons). Suppose a load of cargo containing 45 boxes must be transported via the elevator. Experience has shown that the weight X of a box of this type of cargo follows a probability distribution with mean 200 pounds and standard deviation 55 pounds. What is the probability that all 45 boxes can be loaded onto the freight elevator and transported simultaneously?

5.
(30 marks) Consider the following lotto game. You can pay $10 for one ticket with chances for prizes of various amounts listed below. Assume that there is unlimited number of prizes.


Prize Probability
$2000 0.001
$1000 0.002
$250 0.004
$100 0.01
$50 0.03

(a) A ticket with a prize is said to be a lucky ticket. If you buy one ticket, (4 marks)
what is the probability that it is a lucky ticket?
(b) Let X be the net amount you can win by one ticket. Find ()E X and (10 marks)
()Var X .
(c) If you buy one hundred tickets, what is the probability that you can only (5 marks)
get less than five lucky tickets?
(d) If you buy one hundred tickets, what is the probability that you will lose (8 marks)
less than $100?
(e) What assumption did you made in the calculations in (c) & (d)? (3 marks)
< E N D >

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