| COMSATS Institute of Information TechnologyDepartment of Mathematics| Course Title:| Business Maths & Stats (MTH469)| Class: MBT-3- A, B, C| Resource Person:| Muhammad Hamid Mahmood| Submission: will be informed in class| Assignment # 2

Q1 | What is the preferred way for people to order fast food? A survey was conducted in 2009, but the sample sizes were not reported. Suppose the results, based on a sample of 100 males and 100 females, were as follows:If a respondent is selected at random, what is the probability that he or she a. prefers to order at the drive-through? b. is a male and prefers to order at the drive-through? c. is a male or prefers to order at the drive-through? d. Explain the difference in the results in (b) and (c). e. Given that a respondent is a male, what is the probability that he prefers to order at the drive-through? f. Given that a respondent is a female, what is the probability that she prefers to order at the drive-through? g. Is dining preference independent of gender? Explain.| | |

Q2| A sample of 500 respondents in a large metropolitan area was selected to study consumer behavior. Among the questions asked was “Do you enjoy shopping for clothing?” Of 240 males, 136 answered yes. Of 260 females, 224 answered yes. Construct a contingency table to evaluate the probabilities. What is the probability that a respondent chosen at random a. enjoys shopping for clothing? b. is a female and enjoys shopping for clothing? c. is a female or enjoys shopping for clothing? d. is a male or a female?| | |

Q3| Each year, ratings are compiled concerning the performance of new cars during the first 90 days of use. Suppose that the cars have been categorized according to whether a car needs warranty-related repair (yes or no) and the country in which the company manufacturing a car is based (United States or not United States). Based on the data collected, the probability that the new car needs a...

...phones to school. It is very reasonable because bringing phone toschool potentially disrupts the learning process. Moststudents use cell phones irresponsibly. They use cell phones to talk to their friend during class time. They also use the calculator and camera features in the class as well. Those potentially lead less concentration in the time of learning and teaching process.
Students go to school to learn and behave fair way. Mobile phones provide a large temptation to cheat in tests. They can communicate to anyone and almost anywhere in the world. Because of the small size of the cell phone, students can send a text quietly and discreetly. The text can go unnoticed anywhere to get help on answering tests, homework, and other class assignment. Learning in school is to behave fair not cheating.
Therefore, schools should ban students from bringing their cell phones. However it should be done fairly. In case of an emergency some student need a call for help, providing easy access to phone is better.
NEVER TRY SMOKING
A lot of people, especially teenagers, who do not smoke,always want to try smoking. They know it is bad for them and all, but it is just something they want to try. So they ask one of their smoker friends for a cigarette. Admittedly, they firstly can not light it on their own so they ask his friend to do it. Then they inhale that cigarette and smoke occasionally.
Apparently that makes them the born smokers. Now they do smoke fairly...

...analyzed for strength and conductivity. The results from 100 strands are as follows:
High conductivity
Low conductivity
Strength
High
Low
74
8
15
3
(a) If a strand is randomly selected, what is the probability that its conductivity is high and its strength is high?
P (High conductivity and high strength)= 74/100 =0.74
(b) If a strand is randomly selected, what is the probability that its conductivity is low or its strength is low?
P (Low strength or low conductivity) = P(Low conductivity) + P(Low strength) – P(Low conductivity and low strength) = (15+3)/100 + (8+3)/100 – 3/100 = 0.26
(c) Consider the event that a strand has low conductivity and the event that the strand has low strength. Are these two events mutually exclusive?
No, they are not mutually exclusive.
Because P(Low conductivity) + P(Low strength) = (15+3)/100 + (8+3)/100 = 0.29, which is not equal to P(Low conductivity and low strength).
2-106. A maintenance firm has gathered the following information regarding the failure mechanisms for air conditioning system:
Evidence of electrical failure
Evidence of gas leaks
Yes
No
Yes
55
17
No
32
3
The units without evidence of gas leaks or electrical failure showed other types of failure. If this is a representative sample of AC failure, find the probability
(a) That failure involves a gas leak
P (gas leak) = (55 + 32)/107 = 0.813
(b) That there is evidence of electrical failure given that there was a...

...PROBABILITY DISTRIBUTION
In the world of statistics, we are introduced to the concept of probability. On page 146 of our text, it defines probability as "a value between zero and one, inclusive, describing the relative possibility (chance or likelihood) an event will occur" (Lind, 2012). When we think about how much this concept pops up within our daily lives, we might be shocked to find the results. Oftentimes, we do not think in these terms, but imagine what the probability of us getting behind the wheel of a car twice a day, Monday through Friday, and arriving at work and home safely. Thankfully, the probability for me has been 'one'! This means that up to this point I have made it to work and returned home every day without getting into an accident. While probability might have one outcome with one set of circumstances, this does not mean it will always turn out that way. Using the same example, just because I have arrived at work every day without getting into an accident, this does not mean it will always be true. As I confess with my words, and pray it does stay the same, probability tells me there is room for a different outcome.
In business, we often look at the probability of success or financial gain when making a decision. There are several things to take into consideration such as the experiment, potential outcomes, and possible events. An...

...of observations, which gives each observation equal weight, the mean of a random variable weights each outcome xi according to its probability, pi. The mean also of a random variable provides the long-run average of the variable, or the expected average outcome over many observations.The common symbol for the mean (also known as the expected value of X) is , formally defined by
Variance - The variance of a discrete random variable X measures the spread, or variability, of the distribution, and is defined by
The standard deviation is the square root of the variance.
Expectation - The expected value (or mean) of X, where X is a discrete random variable, is a weighted average of the possible values that X can take, each value being weighted according to the probability of that event occurring. The expected value of X is usually written as E(X) or m.
E(X) = S x P(X = x)
So the expected value is the sum of: [(each of the possible outcomes) × (the probability of the outcome occurring)].In more concrete terms, the expectation is what you would expect the outcome of an experiment to be on average.
2. Define the following;
a) Binomial Distribution - is the discrete probability distribution of the number of successes in a sequence of n independent yes/no experiments, each of which yields success with probability p. Therewith the probability of an event is defined by its binomial...

...CHAPTER 3: PROBABILITY DISTRIBUTION
3.1
RANDOM VARIABLES AND PROBABILITY DISTRIBUTION
Random variables is a quantity resulting from an experiment that, by chance, can assume different values. Examples of random variables are the number of defective light bulbs produced during the week and the heights of the students is a class. Two types of random variables are discrete random variables and continuous random variable.
3.2
DISCRETE RANDOM VARIABLE
A random variable is called a discrete random variable if its set of posibble outcomes is countable. Probability distribution is a listing of all the outcomes of an experiment and the probability associated with each outcome. For example, the probability distribution of rolling a die once is as below: Outcome, x Probability, P(x) 1 1 6 2 1 6 3 1 6 4 1 6 5 1 6 6 1 6
The probability distribution for P(x) for a discrete random variable must satisfy two properties: 1. The values for the probabilities must be from 0 to 1; 0 ≤ ( ) ≤ 1 2. The sum for P(x) must be equal to 1; ∑ ( ) = 1
QMT200
3.2.1 FINDING MEAN AND VARIANCE Mean of X is also referred to as its “expected value”.
= ( ) Where: = ∑[ ( )]
( )=
= (
) − [ ( )]
(
)=
[
( )] = ( )
Example 1 An experiment consists of tossing two coins simultaneously. Write down the sample space. If X is the number of tails observed,...

...BBA (Fall - 2014)
Business Statistics
Theory of Probability
Ahmad
Jalil Ansari
Business Head
Enterprise Solution Division
Random Process
In a random process we know that what outcomes or
events could happen; but we do not know which
particular outcome or event will happen. For
example tossing of coin, rolling of dice, roulette
wheel, changes in valuation in shares, demand of
particular product etc.
Probability
It is the numeric value representing the chance,
likelihood, or possibility a particular event will
occur
It is measured as the fraction between 0 & 1 (or 0%
&100%)
Probability can never exceed 1 and can never be negative
i.e. if P(x) is the probability of occurring event x then 0 ≤
P(x) ≤ 1
Probability = 0 No chance of occurrence of given event
(Impossible event)
Probability = 1 Given event will always occur (Certain
event)
Probability in Business
Betting / Speculation
Estimate the chances that the new product will be
accepted by customers?
Possibility that the planned target will be met
The likelihood that the share prices of the portfolio will
increase
Likelihood of surviving a person till a particular age
Likelihood of surviving a person suffering from a
particular disease
etc. etc.
Probability
It is the numeric value representing the
chance, likelihood, or possibility a particular
event will occur...

...Chapter 1
The Problem and Its Background
Introduction
Changes are permanent thing on earth. Are the people is ready enough to accept the changes on the educational system? The current opening of classes here in the Philippines usually starts from June to March but our lawmakers want to amend the opening of classes. The existing school calendar which spans from June to March is often disrupted as destructive typhoons plague the region during the rainy season that’s why our lawmakers decided to move the opening of classes from September through May to avoid numerous class suspensions and serve to protect the students during strong typhoons. The Department of Education said that it is open to the proposal by some sectors, including lawmakers to move the opening of classes but they want to ensure the comfort of the students in school and stresses the need for a comprehensive study.
While the Department of Education is open on the proposal, some did not welcome this idea. An initial survey on the matter conducted way back in 2009. On the respondents, 66 percent were against the move while 34 percent were in favor. [1] Also, another ground for rejecting the proposal is the traditions celebrated during summer and being not conducive in learning because of hot weather during March. The delay in suspension of classes is one of the reasons why our lawmakers and other sectors in the community urge to move the classes from June to September. Unexpected suspension of classes is...

...IMPACT OF DIVIDEND POLICY ON
SHAREHOLDERS’ VALUE: A STUDY OF INDIAN
FIRMS
Synopsis of the Thesis to be submitted in fulfillment of the requirements for
the Degree of
DOCTOR OF PHILOSOPHY
In
MANAGEMENT
By
Sujata Kapoor
Enrollment No: 064009053
Date of Registration: July 2006
Under the Guidance of
Supervisor: Dr Kanwal Anil
Co-Supervisor: Dr Naseem Abidi
Jaypee Institute of Information Technology, Noida
A-10, SECTOR 62, NOIDA, INDIA (12)
December, 2009
Sujata Kapoor, JBS, JIIT,Dec’ 2009
TABLE OF CONTENTS
S. no.
Contents
Page no.
1.
Introduction
4-9
2.
Review of the literature
9-14
3.
Research objectives
14-15
4.
Research Methodology
15-23
5.
Lintner Model: Analysis and findings
23-24
6.
Factor Analysis and Regression results on
Extracted Factors
24-28
7.
Quadratic Polynomial Regression Analysis
& Findings
28-30
8.
Event study: Analysis & Findings
30-32
9.
Conclusion
32-35
10.
Chapter plan
35-36
11.
Selected References
36-38
12.
Annexure
(III-XX)
2
Sujata Kapoor, JBS, JIIT,Dec’ 2009
KEY TERMS
DIVIDEND PAYOUT RATIO: The percentage of earnings paid to shareholders in dividends.
Calculated as:
DIVIDEND POLICY: The policy a company uses to decide how much it will pay out to shareholders in
dividends.
SHAREHOLDERS’ VALUE: The value delivered to shareholders because of management's ability to
grow earnings, dividends and...

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