Fall 2008 Final - MATH 218 FINAL EXAM Last Name First Name...

MATH 218 FINAL EXAM December 17, 2008
Last Name: _______________________ First Name: _________________________
Student ID Number: _________________ Signature: _________________________
Circle your instructor’s name and session time:
Bruck (11am), (12noon) He (10am) Lin (11am), (12noon) Lytvak (1pm), (2pm)
Mancera (10am), (2pm) Song (11am), (1pm) Yin (9am), (2pm)
INSTRUCTIONS
▪ Answer all ten problems. Numerical answers alone are not sufficient. You must indicate
how you derived them (show work) to obtain full credit . Points may be deducted if you do
not justify your final answer. Please indicate clearly whenever you continue your work on the
back of the page.
▪ When an answer box is provided, put your final answer in the box.
▪ When submitting a numerical answer that is a decimal, use four decimal places of accuracy
after the decimal point.
▪ When submitting a numerical answer that is a fraction, reduce it to lowest terms.
▪ Be sure to include the units in your answer.
▪ If you can not do part a) of some problem, but you need the answer for part b), then you can
get partial credit for showing you know what to do. You could write, “let p be the answer to
a),” and solve b) in terms of p .
▪ The value of a problem is indicated in parentheses following the problem number. The exam
is worth a total of 200 points.
Problem Value Score
1 20
2 20
3 20
4 20
5 20
6 20
7 20
8 20
9 20
10 20
Total 200
1

Problem 1. (20 points) A purchasing department finds that 75% of its special orders are received on
time. Of those orders that are on time, 80% meet specifications completely; of those orders that are late,
60% meet specifications.
a) (4 points) Construct a probability tree for this situation. Be sure to include the events, the
probabilities, conditional probabilities, and joint probabilities, as appropriate.
b) (3 points) Convert the probability tree in part a) into a joint probability table. Be sure to include the
marginal probabilities.
c) (3 points) Find the probability that a randomly selected order is on time and meets specifications.
c)
d) (3 points) Find the probability that a randomly selected order meets specifications.
e) (4 points) If a randomly selected order doesn’t meet the specifications, what is the probability that it
is on time?