251y0480t
ECO251 QBA1
FINAL EXAM
Dec 1, 2004
EXTRA CREDIT TAKE HOME SECTION
Name: _________________________
Student Number: _________________________
1.(5points) To check your work in the 4th Graded Assignment
Enter Minitab.
Put anything in the worksheet. Make sure that ‘enable commands’ in the editor pull-down menu is checked.
Using the ‘file’ pulldown menu, save your worksheet as notmuch.
Use the URL below to get NormArea.txt
http://courses.wcupa.edu/rbove/eco251/251minitab/
Open Normarea. Save it in the same File as where you saved notmuch.
When you are ready to start, use the file menu to open notmuch
Put in the instruction %normarea.
Put in the mean and std deviation at the prompt.
Choose between ‘area to the left’ and ‘area between 2 points’ at the next prompt. If you want ‘area to the
right, use ‘area to the left’ and subtract the result from 1.
For any problem try it first with the original numbers, mean and std deviation. Then convert the numbers to
values of z . Put in a mean of zero and a standard deviation of 1 and the two numbers. Your results for the
two versions of the problem should be very close.
Make sure that the answers that you hand in agree with your results for z .
2. (4 points) If a teller at the Grover’s Corner Bank serves 30 customers per hour, the average amount of
1 60
 2 , c  .5 . c is the parameter of the exponential
time to serve a customer must be two minutes. If 
c 30
distribution.
If a teller at the bank serves 29 customers per hour, the average amount of time to serve a customer must be
60
1 60
29
 2.069 minutes and 
 0.483 . Note also that if know the meaning of F 6 ,
, means that c 
29
c 29
60
Px  6  1  F 6 and this is the probability that it will take more than 6 minutes to serve a customer,
So, take the last digit of your student number and add it to 30 to find out how many customers per hour are
served by tellers at your bank (Use 35 if your number ends in zero) and find.
a) The probability that it takes more than 5 minutes to serve a customer.
b) The probability that it takes no more than 2 minutes to serve a customer.
c) The probability that it takes between 2 and 4 minutes to serve a customer.
3. (4 points) The Negative Binomial distribution gives the probability that there will be x failures before
nq
success n . It has the following probability function. Px  Cnx1n1 p n q x . We also know that  
and
p
2 
nq
. For example, if we want to figure out the probability of 20 tries before our third success n  3
p2
and x  20.
a) If our chance of success is .3, what is the chance that the 5 th success occurs after the 8th failure.
b) What is the average number of failures that will occur before the 5th success?
c) Show that the Geometric distribution is a special case of this distribution by showing under
what conditions Px  and the mean and variance are the same for both distributions.
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