Chapter 7: Random Variables &
Discrete Probability Distributions
7.1 Random Variables & Probability Distributions
Random Variable: is a function or rule that assigns a number to each outcome of an experiment
(ex. Instead of talking about the coin flipping

Chapter 6: Probability
Appendix B Introdution 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, a

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
they spent last week

Chapter 7
7.1 a 0, 1, 2,
b Yes, we can identify the first value (0), the second (1), and so on.
c It is finite, because the number of cars is finite.
d The variable is discrete because it is countable.
7.2 a any value between 0 and several hundred miles

Chapter 6.3
6.47
6.48
6.49
6.50
6.51
6.52
a P(R and R) = .81
b P(L and L) = .01
c P(R and L) + P(L and R) = .09 + .09 = .18
d P(Rand L) + P(L and R) + P(R and R) = .09 + .09 + .81 = .99
6.53 a & b
c
0 right-handers
1
1 right-hander
3
2 right-handers
3
3 r

Chapter 3: Graphical Descriptive Techniques II
3.1 Describe a Set of Interval Data
Example 3.1: Analysis of Long-Distance Telephone Bills:
Following deregulation of telephone service, several new companies were created to compete
in the business of provid

Chapter 4
4.40 First quartile: L25 (15 1)
Second quartile: L50 (15 1)
25
= (16)(.25) = 4; the fourth number is 3.
100
50
= (16)(.5) = 8; the eighth number is 5.
100
75
= (16)(.75) = 12; the twelfth number is 7.
100
Third quartile: L75 (15 1)
4.41 30th per

Chapter 6.1
6.1 a Relative frequency approach
b If the conditions today repeat themselves an infinite number of days rain will fall on 10% of the next days.
6.2 a Subjective approach
b If all the teams in major league baseball have exactly the same player

Chapter 4
4.19 x
s
2
i
x) 2
n 1
2
x
i
n
(x
i
x) 2
n 1
4.21 x
s
i
n
(x
4.20 x
s
x
2
x
i
n
(x
i
x) 2
n 1
9 3 7 4 1 7 5 4 40
=
=5
8
8
[(9 5) 2 (3 5) 2 . (4 5) 2
46
=
= 6.57
7
8 1
4 5 3 6 5 6 5 6 40
=
=5
8
8
[( 4 5) 2 (5 5) 2 . (6 5) 2
8
= = 1.14
7
8

Chapter 1: What is Statistics?
Case 12.1 (Page 4) Pepsis Exclusivity Agreement with a University (see Chapter 12)
In the last few years, colleges and universities have signed exclusivity agreements with a variety of private
companies. These agreements bin

Chapter 2: Graphical Descriptive Techniques I
2.1 Types of Data and Information
Definitions:
A variable is some characteristic of a population or sample. (e.g. student grades) Typically denoted
with a capital letter: X, Y, Z The values of the variable ar

Chapter 11
11.1
H 0 : The drug is not safe and effective
H1 : The drug is safe and effective
11.2
H 0 : I will complete the Ph.D.
H1 : I will not be able to complete the Ph.D.
11.3
H 0 : The batter will hit one deep
H1 : The batter will not hit one deep
1

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 10
10.1 A point estimator is a single value; an interval estimator is a range of values.
10.2 An unbiased estimator of a parameter is an estimator whose expected value equals the
parameter.
10.3
10.4
10.5 An unbiased estimator is consistent if the

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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GrowingKnowing.com 2011
1
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

GrowingKnowing.com 2011
GrowingKnowing.com 2011
1
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