### MATH 318-010 Spring 2006Sample Final

The final exam for this class is open book/open note. You may use a calculator, ruler, pencil, pen and graph paper on the final. You may not use a cell phone calculator, computer, or any other device with the ability to communicate outside the classroom.

How is this sample final related to the actual final exam? Before the last week of class I created a list of final exam questions. Four of those questions are on the sample final and four are on the final exam. Some questions on the final exam will be related to questions on the sample final (e.g. the same question appears on the final with some numbers changed or some information appears on both exams). The average question on the final exam is likely to be easier than the average question on the sample final. Do not expect the questions on the final exam to be of the same type or to cover exactly the same topics as the questions on the sample final.

1. Match the letters of the probability distributions listed below to the appropriate situations for using them.

a) Binomial Probability Distribution
b) Poisson Probability Distribution
c) Uniform Probability Distribution
d) Normal Probability Distribution
e) Standard Normal Probability Distribution
f) Exponential Probability Distribution

_____ The Merry Melodies MusicMaker computer program "sleeps" for a randomly generated amount of time between each musical note played. What's the average sleep time between notes?

_____ This probability distribution is used only when calcluating probabilities for continuous random variables whose probability density functions are shaped like "bell curves".

_____ What is the probability that five people will call the Merry Melodies customer help line in the next 30 minutes?

_____ The Merry Melodies Senior Service Rep. takes a 5 minute coffee break. What is the probability of a call coming in while she's away from her phone?

_____ MusicMaker and Computer Cacaphony are the leading competitors in the computer music market. What is the probability that the next five customers to buy software will choose MusicMaker over Computer Cacaphony?

_____ What is the probability that a customer will use MusicMaker for less than two months before deleting the game from their computer?

2. Shown below is a crosstabulation of which Merry Melodies programmers received bonus pay, organized by gender.

a) Create a joint probability table for programmer bonuses.
b) If a programmer got bonus pay, what is the probability that that programmer was female?

 Bonus No Bonus Female 3 1 Male 7 2

3. Figure 4.17 on page 140 of your text shows a decision tree for the Dante Development Corporation.

a) What is the optimal decision strategy for Dante?
b) Develop a risk profile for this decision strategy.
c) If Dante wins the contract but does no market research, does the MiniMax Regret approach recommend building or selling?

4. Merry Melodies produces two software products: MusicMaker and Computer Cacaphony. They are trying to decide how many copies of each program to produce for the upcoming holiday season.
• Each box of MusicMaker software sold yields \$10 profit. Each Computer Cacaphony sold yields \$6 profit.
• Merry Melodies has enough space in a warehouse for 50 palettes of software. A palette holds 40 copies of MusicMaker software or 100 copies of Computer Cacaphony.
• Projected demand is for 1800 copies of Merry Melodies and 1500 copies of Computer Cacaphony.
• Merry Melodies' lawyers recommend that at least 40% of the software produced be Computer Cacaphony in order to avoid an antitrust suit.
a) Formulate a linear programming problem to decide how many of each to produce.
b) Solve that linear programming problem and give the amounts of each type of software Merry Melodies should produce.