Chapter 6 Notes
Continuous means any value in a range is possible
o Example suppose a stock can have a return of anywhere between 0 and 10 percent
All possible vales (outcomes) are equally likely
o Called a continuous uniform random var.
Area=base X hei
BUS 205
General Normal Distribution Solutions
21) Suppose that in a certain city, the number of days that homes remain on the market before selling is
normally distributed with mean 47.5 and standard deviation 10.27. Use the applet to find the
probability
BUS 205
INDEPENDENCE
Exercise 1: Suppose you choose a registered voter at random from a sample with these characteristics
Gender\Party Democrat Republican Other
Total
Female
40
60
20
120
Male
60
90
30
180
Total
100
150
50
300
a) Are the events A (person c
SUMMARY OF IMPORTANT POINTS FROM Central Limit Theorem Worksheet:
GENERAL
A. The sample mean,
X , is a random variable because it takes different values, depending on the
sample that is chosen.
B. Any random variable, including
X , has a mean, a standard
Solutions to Review Worksheet: Chapters 6 and 7
Chapter 6
1) Suppose that the time it takes for a barista to prepare a cappuccino is continuously uniformly distributed
between 1 and 1.5 minutes. What is the probability that it will take more than 1.4 minu
BUS 205
PROBABILITY CONCEPTS
Age Group
Child
Mature
Older
Young
Total
Female
10
20
30
20
80
Male
20
0
40
30
90
Total
30
20
70
50
170
Note that the fraction of the total that a group of customers comprises is also the probability of choosing a
customer of
SOLUTIONS: Review Worksheet: Chapters 4 & 5
Chapter 5: Discrete Random Variables
1) Suppose that the following information represents the number of days that 100 employees of your company
called in sick over the last year.
x
# of Employees (a) P(X = x) x*
BUS 205 Business Decision Problem
Your company is trying to decide where to locate a sign advertising its services. There are two choices for
locations near Federal Hall: (1) 7th street and (2) Cherry Street.
Since you only have enough resources to put up
Solutions to Binomial Worksheets
Problem: You work in the reservations department of a hotel (or an airline). You have a problem with people
not showing up for the reservations they make, so you are left with empty rooms (seats) that you could have
filled
Chapter 4
Probability
Concepts
1
2
The Connection
Chapter 1-3
Descriptive
Statistics
Chapter 4-6
Probability
Concepts
Chapter 7+
Statistical
Inference
Have data suppose from sample
If wish to generalize to population, must deal with
UNCERTAINTY
To measure
Sampling Distribution of
X
: EXERCISE SOLUTIONS
Problem 1: Suppose we know the distribution of the population, X, representing the price of a certain
product, is normally distributed with mean $350 and standard deviation $30. For a sample of n = 5
from th
Sampling Worksheet Solutions
ACTIVITY # 1
1) B. Differs depending on the sample
2) B. Not be equal to (probably)
3) Sampling Error
ACTIVITY # 2
4) Select a Uniform population. Select n = 2 and press the Sample button. Observe that the mean of
the sample i
Exercise 1
General Instructions:
Region
East
West
North
South
Frequency
80
35
79
62
Relative Frequency
Follow the steps in each exercise. You can work within
this worksheet. When you have finished, click the
Solutions tab to see if your results are correc
WHY IS
DATA-DRIVEN DECISION
MAKING IMPORTANT TO
STUDY?
ARGUMENT 1
Business Analytics/DDDM is important to study
because
Businesses and organizations have
data and need to use that data to
make good decisions.
Source: Dr. DePaolo
QUESTION 1
How strongly ar
What is wrong with data collected in these ways? SOLUTIONS
1) Internet survey invites people by email to participate in a survey about the environment. Those who
really care about the environment are more likely to respond. Those who are not very interest
Example 2
Overbooking Problem
x
9
10
n
10
P(X = x) using Excel formula
0.347
0.197
P(X <= 8) =
P(X > 8) =
P(X > 8) =
0.456
0.544
0.544
Cumulative Probability
Using Cumulative Probability
Using table above
Example 3
Overbooking Problem
x
0
1
2
3
4
5
6
7
8
Collecting
Data
Chapter 1 concepts
Before Get Into Statistics
Need
some terms and definitions
DATA
are facts and figures that are
collected, analyzed and interpreted.
Example:
survey collects data, when all
have completed, will give a data set.
Ways to
Summarizing
& Displaying
Qualitative
Data
Activity 1:
How
would you summarize or display the data resulting from
this question?
I perceive recycling to be:
A. Necessary. I do all that I can to reduce my households
waste and landfill contribution.
B. Confu
BUS 205
The Continuous Uniform Distribution - SOLUTIONS
EXAMPLE 1: Suppose this random variable, X, represents the return from a stock. It can be anywhere
between 0 and 10 percent (not just whole percents) and all of the possible values between 0 and 10 a
BUS 205
Worksheet on Standard Normal Distribution - SOLUTIONS
EXERCISES:
1) 0.5
2) 0.6829
3) P(0 < Z < 1.59) = _0.4441_ . Label each area (left, between, right). Examples are shown.
0.4441
0.5
0.0559
4)
P(-1.59 < Z < 0) = _0.4441_ . Label each area (left,
BUS 205: Chapter 7
Samples & Sampling
Chapter 7 - Sampling
Finally
getting into Statistics
Data
Ch. 1-3
Probability
Ch. 4-6
Statistics
Ch. 7+
Recall:
population
parameter
sample
statistic
Process of Sampling
Use
sample statistics to
estimate the populatio