IND508 OPERATIONS RESEARCH I

Department of Management, UTSC

ECMB11H3Y Quantitative Methods in Economics I L01

Lecture 03 - In Class Exercise Summer 2012Problem 1The Energy Information Administration in the US reported the mean retail price per gallon of regular gasoline was $2.30 in 2006. Suppose the standard deviation was $0.10. (a) What can you say about the % of regular gas sold between $2.10 and $2.50 per gallon? (b) How about between $2.15 and $2.52?

(c) What can you say about the % of regular gas sold between $2.10 and $2.50 per gallon if the price of gas has a bell shaped distribution? (d) What can you say about the % of regular gas sold between $2.20 and $2.50 per gallon if the price of gas has a bell shaped distribution? Problem 2(a) Consider the Tim Horton case (02Lecture-case.pdf). Using Excels Data Analysis Descriptive Statistics tool on question 1 data set of 30 customers (03Lecture-case.xlsx) you get the following output. Do you feel that Store Managers are doing their job in enforcing the 20min rule?

Time Spent at Tim Hortons

Mean18.73333333

Standard Error1.994206167

Median17.5

Mode7

Standard Deviation10.92271702

Sample Variance119.3057471

Kurtosis0.249112574

Skewness0.725353099

Range44

Minimum3

Maximum47

Sum562

Count30

(b) Answer Question 2 in Tim Horton case study.(c) Consider the Tim Horton case study question 1 but suppose there is an additional data point that is 55 minutes, it is an outlier?

Column1

Mean19.87096774

Standard Error2.25843315

Median18

Mode7

Standard Deviation12.57442361

Sample Variance158.116129

Kurtosis0.970853597

Skewness1.021467359

Range52

Minimum3

Maximum55

Sum616

Count31

Problem 3Given 5 equally likely outcomes O1, O2, O3, O4, O5 and events A = {O1, O2}, B = {O3, O4}, C = {O2, O3, O4}

(a) Find P[A], P{B], P[C]

(b) Find P[ A U B]. Are A and B mutually exclusive?

(c) Find P[ AC].

(d) Find P[ A U BC]. Problem 4Given P[A] = 0.3, P[B] = 0.4, P[A B] = 0.2 find P[ AC (A U B)].Problem 5

You go to a casino and there is a game where the dealer rolls a pair of dice. You bet that the total rolled is 6, what is probability of you winning?Problem 6

The project approval process in a certain corporation follows the circuit pictured below. If manager a approves, the project is approved irregardless of what the other mangers do. If manager a does not approve the project, but manager b approves the project, then it forwarded to both managers c and d. If either c or d approves, then the project is a go. Suppose that each manager has a probability p = 0.7 of approving the project and that everyone comes to the decision independently, what is the probability that a project will be approved in the corporation (8 marks)

Let outcome a = manager a approves, A = manager a not approve. Same goes for b,c,d.

Probability manager approves = p and not approve = . Circle all events lead to project not getting approve.

0 approveabcd

1 approveAbcdaBcdabCdabcD

2 approveABcdAbCdAbcDaBCdaBcDabCD

3 approveABCdABcDAbCDaBCD

4 approveABCD

Problem 6There are 50 workers in a small company. 5 workers completed work late. 6 workers made defective parts. 2 workers were late and made defective parts.

(a) What is probability that a worker is late in this company?

(b) What is probability that a worker made defective parts in this company?

(c) If there were 100 workers in this company, how many would either be late or made defective parts or both?

(d) Are the events late and made defective parts mutually exclusive?

2

_1237649034.unknown