Efficient Rate Example and The Payback Period for Projects
Problem
Admiral Bills believes that the boxes of cake mix are not being filled using the most
efficient rate.
Methodology
First I used normal distribution to calculate the percent and number of go
Sammys Exterminators Regression Example
Regression One
Salary = 44,615 + 15,206 (Gender)
(51,525) (3,778)
(5,604) R^2=0.021= 2.1%
Sammy pays $44,615 + $15,206 if you are a man.
Regression Two
Salary = -554 + 6,737 (Experience)
(41,555) (4,368) (484)
R^2 =
Mimis Orlando Shuttle Calculating Profit Example
Problem
Mimis Orlando Shuttle is losing money because of a recent fuel crisis and a problem
with no-show reservations. She doesnt overbook or charge a cancellation fee.
She must find a way to design a new r
Regression Analysis
Regression 1
Salary = 87,690 + 3,969 (Experience) 85,171 (Expert) + 1,855 (Gender)
(26,428) (5021)
R^2 = 0.744 = 74.4%
(333)
(3825)
(2910)
Sammy pays $87,690 + $3,969 per year of experience $85,171 if you are
not an expert + $1,855 if
Hogan Industries Probability Example
Problem
The CEO of Hogan Industries, Holly Hogan, believes that there must be a better way
to save money on expensive valves, while keeping the risk of catastrophe to a
minimum, by utilizing a system of mixed-quality v
The Mean of a Binomial
o The mean of a Binomial, in addition to being the sum of (x * P(x) is also simply n*p
And the Standard Deviation in addition to being the square root of the sum of (xmean) squared * P(x) is the square root of n*p*q
Geometric Distri
Uniform Distribution
The probability of the second hand being between any 2 adjacent numbers would be 1/12. The
collection of the outcomes of the second hand is a uniform distribution.
o In a Uniform Distribution, all outcomes (of equal width) are equally
Tree Statistics
o Lets take a look at a TreeORIGINAL EXAMPLE
The Addition Rule
o The probability that one or the other of two events will occur is:
o P (A or B) =P(A) + P(B) - P(A and B)
o This subtraction eliminates/accounts for any double counting that
Hogan Industries Solution and Calculation
a. The yearly cost of maintaining the current system is $142,985.92
= (cost of valves including labor + initial cost per year) =
($130,985.92 + $12,000)
b. For my proposed system, I predict a catastrophe to occur
The Probability Rules Common Mistakes
1. Using the wrong formula, especially since the Multiplication Rule is used for And &
our intuition is And indicates the need for the Addition Rule
2. Adding rather than multiplying fractions in the Multiplication Ru
Probability Distributions
As (perhaps) the name suggests, a Probability Distribution is a collection
(distribution) of the probabilities of events occurring.
o Better stated, a collection of the events (outcomes) and their probabilities.
Discrete Random V
Probability Distribution Rules:
1.Probabilities cannot be negative, nor can they be greater than one
2.The outcomes that can occur cannot overlap - Mutually Exclusive
3.All the outcomes must be accounted for - Collectively Exhaustive
Mutually Exclusive:
A
Questions & Answers to Proportions
o What proportion of the drivers failed the test
o P (F)
=
.23
o What percentage of the drivers who Passed (77) the test are Drunk (5)
o P (D | P) = 5/77= .065
o What proportion of the drivers who Failed (23) the test we
Rolling Dice Example - Conditional Probability
If we are to roll 2 dice and roll a 1 with the first one, what is the probability we roll a
1 with the second one?
o Is it 1/5 or maybe 0/5? or 0/6? or 1/6
It IS 1/6!
But thats different from the Men and Ladi
Probability Distribution
The MEAN of a Probability Distribution is the sum of (each value times its respective
probability) (x * P(x )
The STANDARD DEVIATION of a Probability Distribution is The Square root of:
the sum of [(each value minus the MEAN) squa
The Central Limit Theorem
Assume you are to flip coins.
Heads = 1
Tails = 0
If you toss a coin once, what would the AVERAGE be: either 0 or 1.
If you toss a coin twice, what could the AVERAGE be: it could be zero (2 tails) with a
probability of .25, it co
Testing in Decision Making:
o What percentage of the drivers who Passed the test are Drunk?
o P (D | P)
=
?
o What proportion of the drivers failed the test
o P (F)
=
?
o What proportion of the drivers who Failed the test were Sober
o P (S | F)
=
?
Other
Statistic Definitions
Data - numeric information we collect through measurement, observations, or counts.
Experiment act of obtaining data
A simulation uses a mathematical model to reproduce conditions of an experiment
Census is a count or measurement of
Standard Deviation in Probability Distribution
Why the confusing new way?
Using the old method, to calculate the mean we would need to list all (123)
numbers, add them up and divide by 123.
There are 33 of the number 19, 12 of the number 20 Wouldnt you ju
Probability of Success
o Using the newly discovered Binomial formula, find the Probability Mary gets 4 As, 3As
and 2 As
o P(4) =5*.8*.8*.8*.8*.2 = .4096
o P(3) =10*.8*.8*.8*.2*.2 = .2048
o P(2) =10*.8*.8*.2*.2*.2 = .0512
Binomial Distribution Tables
o Int
Example of Good Value Proposition - ABC Company can improve its market
share by a minimum of 4 percentage points in a one-year period in its San
Francisco & Dallas markets by implementing our customer satisfaction and
retention training for its customer s
1. Inbound Telemarketing (Prospect calls the company) This is a source
of locating prospects whereby the prospect calls the company to get
information.
2. Outbound Telemarketing (Salesperson contacts the prospect) this is a
source of locating prospects wh
Gathering Pre-Call Information - About the Company:
1. Type of Business
2. History of Business
3. Current Strategy & Performance
4. Number of Employees
5. Target Markets Served
6. Products & Services Offered
7. Key Competitors
Gathering Pre-Call Informati
Sales Dialogue - Business conversations between buyers and sellers that occur as salespeople
attempt to initiate, develop, and enhance customer relationships. Sales dialogue should be
customer-focused and have a clear purpose.
1. Sales Dialogue occurs ove
Written Sales Proposals A complete self-contained sales presentation on paper, often
accompanied by other verbal sales presentations before or after the proposal is delivered.
Example: A response to a Request for Proposal (RFP)
1. Writing Effective Propos