251x0821 3/26/08 (Revised)
ECO251 QBA1
SECOND EXAM
March 27, 2008
TAKE HOME SECTION
Name: _________________________
Student Number: _________________________
Throughout this exam show your work! Neatness counts! Please indicate clearly what sections of the
problem you are answering and what formulas you are using.
Part III. Do all the Following (12+ Points) Show your work!
1. Seymour Butz’s student number is 976543
Take the following set of numbers: and the probabilities below
x
P x 
10
.16
20
.17
30
.18
42
.19
53
.20
64
__
75
__
and use the second to last digit of your Student Number to provide the first digit of all seven numbers so
that they become 3 digit numbers, so that, for Seymour, the numbers would become 410, 420, 430, 442,
453, 464 and 475. Now compute the last two probabilities by putting the last digit of your student number
divided by 100 in the first blank. For Seymour, this would mean that he will write in .03. In the second
blank, put in whatever you need to make the distribution valid and explain how you got that number.
Compute a population standard deviation using your probabilities. (2) Find the probability that x is an
even number and the median of the distribution. Again show your work. (1)
2. Compute a sample standard deviation for your x column. Ignore the probabilities. (2)
[5]
3. Assume that we roll a pair of dice. Use x for the amount on top of the first die, y for the amount on top
of the second die and w for their sum. Let zo be the value of the last digit of your student number plus 2.
Seymour Butz’s student number is 976543. For Seymour this means zo  5 .
Let event A be w  z0  . Let event B be y is an even number . Let event C be w  z0  . Make sure that
I know what z0 is and show your work. Find (1 each): [12]
a) P A
b) PC 
 
c) P B C
d) PB  C 
e) PB  C 
 
f) P C B

g) P B  C

1
251x0821 3/26/08 (Revised)
4. (Moore et al) 5% of male high school athletes (in basketball, football or baseball) compete in college. Of
those who compete in college, 1.7% go on to major league sports. 40% of the athletes who compete in both
high school and college and enter major leagues last more than three years. The probability that a high
school athlete who does not compete in college goes on to professional play is .0001.
Although the numbers given above are probably correct, modify the probabilities as follows: Seymour
Butz’s student number is 976543. Take the last digit of your student number and add it to 5%, so, for
example, Seymour will say that (5+3) % = 6% of male high school athletes compete in college; then take
the same number and add it to the 1 in .0001, so, for example, Seymour will say that .0001 + .0003 = .0004
is the probability that a high school athlete who does not compete in college goes on to professional play.
Let A be the event that a high school athlete competes in college. Let B be the event that a high-school
athlete competes professionally. Let C be the event that a high-school athlete has a professional career of
more than 3 years. Use these in your answer. (2 points extra credit for each part)
a) Identify your four probabilities as given the problem and modified by you in terms of events A , B and
C . That is to say probabilities like PB  C  , P B  C , P B C or P A  B  C  . (I do not want to

  
imply that any of these appear in the problem)
b) What is the probability that a high school athlete will play in college and then have a major league career
of more than three years?
c) What is the probability that a high school athlete will play professional sports?
d) What proportion of professional athletes competed in college?
2