### Homework 1

Click on the assignment title to access it. Attach your homework solutions. The preferred format is Excel â€” one workbook â€” with each problem in its own sheet and each sheet labeled according to the problem.

Please submit only one document/workbook per assignment.

### Questions

#### Chapter 2 – Question 14

A student taking Management Science 301 at East Haven University will receive one of the five possible grades for the course: A, B, C, D, or F. The distribution of grades over the past two years is as follows:

A 80
B 75
C 90
D 30
F 25
Total 300

If this past distribution is a good indicator of future grades, what is the probability of a student receiving a C in the course?

#### Chapter 2 – Question 15

A silver dollar is flipped twice. Calculate the probability of each of the following occurring:

1. a head on the first flip
2. a tail on the second flip given that the first toss was a head
3. two tails
4. a tail on the first and a head on the second
5. a tail on the first and a head on the second or a head on the first and a tail on the second
6. at least one head on the two flips

#### Chapter 2 – Question 29

Which of the following are probability distributions? Why?

1. RANDOM VARIABLE X PROBABILITY
2 0.1
â€“1 0.2
0 0.3
1 0.25
2 0.15
2. RANDOM VARIABLE Y PROBABILITY
1 1.1
1.5 0.2
2 0.3
2. 0.25
3 â€“1.25
3. RANDOM VARIABLE Z PROBABILITY
1 0.1
2 0.2
3 0.3
4 0.4
5 0.0

#### Chapter 2 – Question 31

What are the expected value and variance of the following probability distribution?

RANDOM VARIABLE X PROBABILITY
1 0.05
2 0.05
3 0.10
4 0.10
5 0.15
6 0.15
7 0.25
8 0.15

#### Chapter 2 – Question 41

The time to complete a construction project is normally distributed with a mean of 60 weeks and a standard deviation of 4 weeks.

1. What is the probability the project will be finished in 62 weeks or less?
2. What is the probability the project will be finished in 66 weeks or less?
3. What is the probability the project will take longer than 65 weeks?

#### Chapter 2 – Question 48

Policy Pollsters is a market research firm specializing in political polls. Records indicate in past elections, when a candidate was elected, Policy Pollsters had accurately predicted this 80 percent of the time and they were wrong 20% of the time. Records also show for losing candidates, Policy Pollsters accurately predicted they would lose 90 percent of the time and they were only wrong 10% of the time. Before the poll is taken, there is a 50% chance of winning the election. If Policy Pollsters predicts a candidate will win the election, what is the probability that the candidate will actually win? If Policy Pollsters predicts that a candidate will lose the election, what is the probability that the candidate will actually lose?