Introduction to Business Analytics
Homework 1
Click on the assignment title to access it. Attach your homework solutions. The preferred format is Excel — one workbook — with each problem in its own sheet and each sheet labeled according to the problem.
To receive full credit, you need to show the solution process — not just the answers. Add comments/text boxes to your spreadsheet to explain details as necessary.
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:
| GRADE | NUMBER OF STUDENTS |
|---|---|
| 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:
- a head on the first flip
- a tail on the second flip given that the first toss was a head
- two tails
- a tail on the first and a head on the second
- a tail on the first and a head on the second or a head on the first and a tail on the second
- at least one head on the two flips
Chapter 2 – Question 29
Which of the following are probability distributions? Why?
-
RANDOM VARIABLE X PROBABILITY 2 0.1 –1 0.2 0 0.3 1 0.25 2 0.15 -
RANDOM VARIABLE Y PROBABILITY 1 1.1 1.5 0.2 2 0.3 2. 0.25 3 –1.25 -
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.
- What is the probability the project will be finished in 62 weeks or less?
- What is the probability the project will be finished in 66 weeks or less?
- 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?
