1. Explain the difference between quantitative and qualitative analysis from the manager's point of view.
2. Explain the difference between mutually exclusive and independent events. Can a pair of events be both mutually exclusive and independent?
3. Explain the transformation from any normal distribution to the standard normal.
4. A video rental store has two video cameras available for customers to rent. Historically, demand for cameras has followed this distribution. The revenue per rental is $40. If a customer wants a camera and none is available, the store gives a $15 coupon for tape rental.
| Demand |
Relative frequency |
Revenue |
Cost |
| 0 |
0.35 |
0 |
0 |
| 1 |
0.3 |
40 |
0 |
| 2 |
0.2 |
80 |
0 |
| 3 |
0.1 |
80 |
15 |
| 4 |
0.05 |
80 |
30 |
a. What is the expected demand?
b. What is the expected revenue?
c. What is the expected cost?
d. What is the expected profit?
5. The time it takes to travel from home to the office is normally distributed with mu = 25 minutes and standard deviation = 5 minutes.
a. What is the probability the trip takes more than 20 minutes?
b. What is the probability the trip takes less than 15 minutes.
c. What is the probability the trip takes between 30 and 35 minutes?
d. What is the probability the trip takes more than 40 minutes?
6. A payoff table is given as.
|
State of Nature |
| Decision |
s1 |
s2 |
s3 |
| d1 |
250 |
750 |
500 |
| d2 |
300 |
-250 |
1200 |
| d3 |
500 |
500 |
600 |
a. What choice should be made by the optimistic decision maker?
b. What choice should be made by the conservative decision maker?
c. What decision should be made under minimax regret?
d. If the probabilities of d1, d2, and d3 are 0.2, 0.5, and 0.3, respectively, then what choice should be made under expected value?
e. What is the EVPI?
7. For the payoff table below, the decision maker will use P(st) = 0.15, P(s2) = 0.5, and P(s3) = 0.35.
|
State of Nature |
| Decision |
s1 |
s2 |
s3 |
| d1 |
-5000 |
1000 |
10000 |
| d2 |
-15000 |
-2000 |
40000 |
a. What alternative would be chosen according to expected value?
8. Use a four period moving average to forecast attendance at baseball games. Historical records show: 5346, 7812, 6513, 5783, 5982, 6519, 6283, 5577, 6712, 7345