FORMULA SHEET QNM 222
Frequency Distribution
2",>_n, k = #of classes
Class width= (highest-lowest)/k
Population mean (ungrouped)
_ E:
H N
Samgle mean (ungrouped)
X:
:2
Population mean (grouped data)
l1 = Zia
N
Sample mean (grouped data)
'7; = m
11
Raw Dat
NOTATION
L = List price
d = Single discount rate
d L = Amount of trade discount
de = Single equivalent discount
rate to a series of discount rates
N = Net price
C = Cost
M = Markup
S = Selling price
(or regular selling price)
D = Markdown
BE = Break-even
QNM106: MATHEMATICS FOR BUSINESS AND FINANCE FALL 2016
1
Text Book
Mathematics of Business and Finance, 2nd Edition Daisley, Kugathasan, Huysmans .published by
Vretta Inc.
The new textbook which includes the Access Code can be purchased from the bookstore
Appendix B Introduction into Probability (Ch. 6)
Counting Rules for Multiple-Step Experiments:
If an experiment can be described as a sequence of k steps with n1 possible outcomes on the first
step, n2 possible outcomes on the second step, and so on, then
Chapter 9
9.1a. 1/6
b. 1/6
9.2 a P( X 1) =P(1,1)= 1/36
b P( X 6) = P(6,6) = 1/36
9.3a P( X = 1) = (1/6) 5 = .0001286
b P( X = 6) = (1/6) 5 = .0001286
9.4 The variance of X is smaller than the variance of X.
9.5 The sampling distribution of the mean is nor
Chapter 6: Probability
Appendix B Introduction into Probability
Counting Rules for Multiple-Step Experiments:
If an experiment can be described as a sequence of k steps with n1 possible outcomes on the first
step, n2 possible outcomes on the second step,
Chapter 9: Sampling Distributions
9.1 Sampling Distribution
Central Limit Theorem: The sampling distribution of the mean of a random sample drawn from any
population is approximately normal for a sufficiently large sample size (n > 30). The larger the
sam
Chapter 4: Numerical Descriptive Techniques
4.1 Measures of Central Location
Mean: the average of a group of numbers
Population Mean
=
=
+ +
Sample Mean
=
=
+ +
Example 4.1.1: A sample of 10 students from your business class was asked how many hours
Terminologies: (up to Ch12)
Population mean
Sample mean
Population standard deviation
Sample standard deviation
Population proportion
Sample proportion
Sample size
Error of estimation
Null hypothesis
Alternative hypothesis
Test Statistic: ( z critical &
Chapter 9
P p
9.30a P( P > .60) = P
p(1 p) / n
= P(Z > 3.46) = 0
(.5)(1 .5) / 300
.60 .5
P p
.60 .55
= P(Z > 1.74) = 1 P(Z < 1.74)
b. P( P > .60) = P
p(1 p) / n
(.
55
)(
1
.
55
)
/
300
= 1 .9591 = .0409
P p
c. P( P > .60) = P
p(1 p) / n
= P(Z > 0)
The entries in thla table are the
probabilities that a standard normal
random varlable is beta-mean 0 and z
0.0
0.1
0.2
0.3
0.4
0.5
0.3
0.?
0.9
1.0
1.1
1.2
1.3
1.4
1.5
1.3
1.?
1.3
1.9
2.0
2.1
2.2
2.3
2.4
2.5
2.3
2.?
2.3
2.9
3.0
3.1
3.2
3.3
3.4
3.5
4.0
4.5
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Normal distributions
Wake-up!
Normal distribution calculations are used
constantly in the rest of the course, you must
conquer this topic
Normal distributions are common
There are methods to use normal dis
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Small Samples
If your sample size is below 30, this is a small sample
so use the t table, not z.
Decision rule uses =t.inv instead of =normsinv
Excel 2010: 2-tail: t =t.inv.2t(alpha, degrees of
freedom)
E
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Binomial probabilities
Your choice is between success and failure
You toss a coin and want it to come up tails
Tails is success, heads is failure
Although you have only 2 conditions: success or failure,
i
STATISTICAL ESTIMATION
STATISTICAL INFERENCE is the process by which statisticians make
predictions about a population on the basis of samples
STATISTICAL ESTIMATION is the use of sample data to estimate certain
unknown quantities of the population
POINT
INTRODUCTION TO STATISTICS
WORD LIST
Population
Sample
Descriptive Statistics
Probability
Inferential statistics
Nominal Data
Ordinal Data
Interval Data
Ratio Data
DATA LEVELS
1.Nominal Data:
weakest of all data types.
Used to classify into categories
Cat
PROBABILITY RULES
1. Louis has been shopping for a calculator and has decided to buy a scientific
model. The probability that he will buy the HP model is 1/9 and the
probability that he will buy the TI is 4/9. What is the probability that he will
buy eith
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Binomial probabilities
Your choice is between success and failure
You toss a coin and want it to come up tails
Tails is success, heads is failure
Although you have only 2 conditions: success or failure,
i
PROPORTIONS
1. From past experience it is known that 70% of all airplane tickets sold are
round trip tickets. A random sample of 100 passengers is taken and found
that 72% of the passengers had purchased round trip tickets. At the 0.05
level of significan
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Sample proportions
Standard error for proportion =
z score =
ps is sample proportion.
p is population proportion.
p is standard error
n is the sample size.
To qualify to use the formula: np 5 and n(1-p)
5
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Correlation and Regression
Correlation shows relationships between
variables.
This is important.
All professionals want to understand relationships.
If I double client calls, do I double my commissions?
I
THE CENTRAL LIMIT THEOREM
If large random samples of size n (usually samples of size n>30)
are taken from a population with a mean u and a standard
deviation , and if a sample mean is computed for each
sample, then the following three things will be true
PROBABILITY DISTRIBUTIONS
WORD LIST
1. Probability distribution
2. Random Variable
3. Discrete Random Variable
4. Continuous Random Variable
5. Binomial Probability Distribution
6. Discrete Probability Distribution
7. Continuous Probability Distribution
8
DESCRIPTIVE STATISTICS
CREATING GRAPHS AND TABLES
WORD LIST
1. Class
2. Frequency
3. Frequency Distribution
4. Relative Frequency Distribution
5. Cumulative Frequency Distribution
6. Relative Frequency Distribution
7. Class Mark
RULES FOR CONSTRUCTING TAB