04 Jun Question ECON 3400 Final Exam 1. Probability(15 Points)
Question
ECON 3400
Final Exam
1. Probability(15 Points)
Of the cars on a used car lot, 80% have air conditioning (AC) and 50% have a GPS. 30% of the
cars have both.
a. Fill the following contingency table. (5 points)
AC
GPS
No AC
Total
0.3
0.5
0.8
1.0
No GPS
Total
b. What is the probability that a car has a GPS, given that it has AC?
i.e., we want to find P (GPS | AC) (5 points)
c. What is the probability that a car has either a GPS or AC?
i.e., we want to find P (GPS AC) (5 points)
2. Discrete Probability Distribution (20 Points)
The J.R. Ryland Computer Company is considering a plant expansion to enable the company
to begin production of a new computer product. The companys president must determine
whether to make the expansion a medium- or large- scale project. Demand for the new
product is uncertain, which for planning purposes may be low demand, medium demand, or
high demand. The probability estimates for demand are .20, .50, and .30, respectively. Letting
x and y indicate the annual profit in thousands of dollars, the firms planners developed the
following profit forecasts for the medium- and large- scale expansion projects.
Demand
Medium-Scale
Expansion Profit
(x)
50
Large-Scale
Expansion Profit
(y)
0
Medium 0.50
150
100
High
200
300
Low
Probability of
Demand
P(i), i:{x,y}
0.20
0.30
a. Compute the expected value for the profit associated with the two expansion alternatives.
Which decision is preferred for the objective of maximizing the expected profit? (10
points)
b. Compute the variance for the profit associate with two expansion alternatives. Which
decision is preferred for the objective of minimizing the risk of uncertainty? (10 points)
2
3. Binomial Probability Distribution (15 Points)
The Center for Medicare and Medical Services reported that there were 295,000 appeals for
hospitalization and other Part A Medicare service. For this group, 40% of first-round appeals
were successful (The Wall Street Journal, October 22, 2012). Suppose 10 first-round appeals
have just been received by a Medicare appeal office.
a. Compute the probability that none of the appeals will be successful. (5 points)
b. Compute the probability that exactly one of the appeals will be successful. (5 points)
c. What is the probability that more than half of the appeals will be successful?(5 points)
4. (4 Points * 5 = 20 Points)
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