Sample of Non-Cumulative Exam #2

Business Analytics I

Exam #1 Antony Davies, Ph.D. Summer 2009 May 20, 2009

This exam is due at the start of class on Wednesday, May 20, 2009.

You may work on this exam alone, or you may work in a group of no more than two people. If you work in a group, submit only one copy of the exam answers.

Sources you may consult in completing the exam:

 A calculator.  Excel (including the probabilities worksheet I provided).  Your text.  Your notes.  Past assignments and answers (from the website).

Instructions

1. You may not consult any sources other than those listed above. 2. Unless told otherwise, do not use information from one question to answer another. 3. Report your answers on the answers sheet. Write your answer in the space provided. Where applicable, show your work in the space provided. 4. Do not provide additional verbal qualifications to your answers. If you feel the need to explain why your answer is correct or conditions under which your answer is correct, then your answer is likely incorrect. 5. Prior to the start of class on the due date, hand in this page and the answer sheets. Exams not handed in by the start of class receive grades of zero.

Please affirm your agreement with the following statement by signing after you complete the exam.

In accordance with Duquesne’s honor code, I attest that I neither received nor offered unauthorized assistance in answering the questions on this exam. If I am a member of a team, I further attest that I have seen and agree with the contribution ratings shown above, and that I have seen and agree with the exam answers my team has submitted. Name(s): ______

On these pages, write your final answer and then show all of your work.

Question #1 Answer ______

Work Question #4 Answer ______

Work Question #8 Answer ______

Question #12 Answer ______Work

Question #16 Answer ______Work

Work Questions 1 through 3 refer to the scenario below.

In the two upcoming basketball games, the probability that UTC will defeat Marshall is 0.48, and the probability that UTC will defeat Furman is 0.55. The probability that UTC will defeat both opponents is 0.3465.

1 What is the probability that UTC will defeat Furman assuming that they defeat Marshall?

2 What is the probability that UTC will win at least one of the games?

3 What is the probability of UTC winning both games?

4 In a city, 60% of the residents live in houses and 40% of the residents live in apartments. Of the people who live in houses, 20% own their own business. Of the people who live in apartments, 10% own their own business. If a person owns his or her own business, find the probability that he or she lives in a house.

Questions 5 and 6 refer to the scenario below.

A very short quiz has one multiple-choice question with five possible choices (a, b, c, d, e) and one true or false question. Assume you are taking the quiz but do not have any idea what the correct answer is to either question, but you mark an answer anyway.

5 What is the probability that you have given the correct answer to both questions?

6 What is the probability that one or both of the two answers is correct?

7 Tammy is a general contractor and has submitted two bids for two projects (A and B). The probability of her winning the bid for project A is 0.65. The probability of her winning the bid for project B is 0.77. The probability of her winning at least one of the bids is 0.90. What is the probability that she will win both bids?

8 A corporation has 15,000 employees. Sixty-two percent of the employees are male. Twenty-three percent of the employees earn more than $30,000 a year. Eighteen percent of the employees are male and earn more than $30,000 a year. What is the probability of an employee earning more than $30,000 per year given that the employee is a female?

Questions 9 through 11 refer to the scenario below.

The following chart shows the frequency distribution for the speeds of a sample of automobiles traveling on an interstate highway. Speed (mph) Frequency 50 – 54 2 55 – 59 4 60 – 64 5 65 – 69 10 70 – 74 9 75 – 79 5 Total: 35

9 What is the sample mean?

10 What is the sample variance? 11 What is the sample standard deviation? Questions 12 and 13 refer to the scenario below.

Dell conducted motion studies in an attempt to measure the time required for a worker to assemble a laptop computer. A sample of fifteen workers achieved the following times (in minutes).

28 25 27 26 20 25 24 20 25 20 19 22 10 21 20

12 Based on this sample information, what is the minimum probability that a given worker will be able to construct a computer in no less than 15 and no more than 30 minutes?

13 Based on this sample information, what is the maximum probability that a given worker will take less than 15 minutes or longer than 30 minutes?

Questions 14 through 16 refer to the scenario below.

Your employer has asked you to perform an analysis of the impact of the firm’s telemarketing activities. Management suspects that the telemarketing effort is not impacting sales. To test this, the telemarketers are told to choose from among three prepared scripts: Long, Medium, and Short. The long script takes two minutes to read and gives details on product features and payment plans. The medium script takes one minute to read and gives details on product features only. The short script takes thirty-seconds to read and only gives an overview of the product.

Management believes that, if the telemarketing effort is having no effect, you will see no difference in sales from using the long script versus using the short script.

For each telemarketing call, you record one of three results: Sale, No Sale, or Eventual Sale. If the customer agrees to purchase when the telemarketer calls, you record the call as a sale. If the customer does not purchase when the telemarketer calls but does purchase within 30 days after the call, you record the call as eventual sale. If the customer does not purchase, you record the call as no sale.

The data you collected is shown in the table below

Long Script Medium Script Short Script Sale 107 152 75 Eventual Sale 215 325 105 No Sale 301 415 259

14 What is the probability of a telemarketer making a sale given that he uses the long script?

15 What is the probability of a telemarketer making a sale given that he uses the short script?

16 Suppose we regard Sale and Eventual Sale as the same outcome. Now, comparing the combined outcome “Sale/Eventual Sale” to the outcome “No Sale,” by how much does use of the long form improve the chances of a sale over the use of the short form? Questions 17 and 18 refer to the scenario below.

Local law enforcement recently conducted a sobriety test. Police set up a roadblock at 1:00 am on a Friday night and randomly tested drivers for blood alcohol content. Out of 72 drivers, 6 tested above the legal limit for blood alcohol (making them “legally drunk”). Separately, the Department of Transportation is testing computer software that monitors traffic through video cameras placed along the highway. The software is designed to monitor cars’ left-right movements as the cars pass within view of the cameras. The software’s purpose is to detect erratic driving. The DOT conducted tests in which volunteer drivers were given enough alcohol to make them legally drunk. Out of 143 drunk drivers, the software determined that 122 were driving erratically. As a control, another 98 sober drivers were asked to participate in the experiment. Of these, the software determined that 9 drove erratically.

17 What is the probability of the software determining that a driver is drunk (i.e. detecting that the driver is driving erratically) when, in fact, the driver is not drunk?

18 Police use the software and pull over someone who is driving erratically. The person claims that he is sober. What is the probability that the person is lying?