MGMT 2340
Section
W01
Business Statistics I
Instructor:
E. Mark Leany
contact via
Blackboard
online.uen.org
alternately:
[email protected]
Continuous Probability Distributions
Chapter 7
218

GOALS
1.
Understand the difference between discrete and continuous
distributions.
2.
Compute the mean and the standard deviation for a
uniform
distribution
.
3.
Compute probabilities by using the uniform distribution.
4.
List the characteristics of the
normal probability distribution
.
5.
Define and calculate z values.
6.
Determine the probability an observation is between two points on a
normal probability distribution.
7.
Determine the probability an observation is above (or below) a point
on a normal probability distribution.
8.
Use the normal probability distribution to approximate the binomial
distribution.
218
Binomial – Shapes for Varying
n
(
S
constant)
197
Total Area = 1.00
Area = Height x Width = Probability

The Uniform Distribution
The uniform probability
distribution is perhaps the
simplest distribution
for a
continuous random
variable
.
This distribution is
rectangular
in shape
and is defined by
minimum and maximum
values.
Events are
Equally Likely
(hence Uniform)
What do we know about area?
Sum of Area =
1
219
Area of a Line = 0.00
The Uniform Distribution – Mean and
Standard Deviation
220

Southwest Arizona State University provides bus service to students while
they are on campus. A bus arrives at the North Main Street and College
Drive stop every 30 minutes between 6 A.M. and 11 P.M. during
weekdays. Students arrive at the bus stop at random times. The time
that a student waits is uniformly distributed from 0 to 30 minutes.
1.
Draw a graph of this distribution.
2.
Show that the area of this uniform distribution is 1.00.
3.
How long will a student “typically” have to wait for a bus? In other words
what is the mean waiting time?
4.
What is the standard deviation of the waiting times?
5.
What is the probability a student will wait more than 25 minutes
6.
What is the probability a student will wait between 10 and 20 minutes?
The Uniform Distribution - Example
221
The Uniform Distribution - Example
1. Draw a graph of this distribution.
221
3
0
.
0
0
30
1
1
)
(
!
0
!
0
!
a
b
x
P

The Uniform Distribution - Example
2. Show that the area of this distribution is 1.00
221
The Uniform Distribution - Example
3. How long will a student
“typically” have to wait for a
bus? In other words what is
the mean waiting time?
What is the standard
deviation of the waiting
times?
221

The Uniform Distribution - Example
4. What is the probability
a student will wait
more than 25
minutes?

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- Spring '11
- Leany
- Normal Distribution