11/9/2010

1

Quiz 2 covered materials in

•Chapter 5

•Chapter 6

•Cha

p

ter 7

p

Normal Probability

Distribution

Chapter 6

Continuous Probability

Distribution

Normal Distribution Uniform Distribution

Normal Distribution is symmetrical and bell

shaped, implying that most values tend to

cluster around the mean, equal to median.

The uniform distribution is symmetrical

and therefore the mean = median.

Normal Probability Distribution

The focus is on a

continuous,

bell-shaped

distribution

distribution

Discuss the

properties

Properties

1. The shape is determines by mean, Pand

standard deviation, V

2. The highest point on the normal curve is

located at the mean, which is also the

median and the mode of the distribution.

3. The normal distribution is symmetrical: the

curve’s shape to the left of the mean is the

mirror image of its shape to the right of the

mean. Thus, mean = median

4The tails of the normalcurveextend toinfinity

4

.

The

tails

of

the

normal

curve

extend

to

infinity

in both directions and never touch the

horizontal axis. Thus, it has an infinite range.

-f< X < +f

5. However, the tails get close enough to the

horizontal axis quickly enough to ensure that

the total area under the normal curve equals

1.

6. Since the normal curve is symmetrical, the

area under the normal curve to the right of

the mean (P) equals the area under the

normal curve to the left of the mean, and

each of these areas equals 0.5.

Normal Probability Distribution

When a mathematical

expression is available to

represent a continuous variable,

the probability that various

values occur

within certain ranges

or intervalscan be calculated.

www.notesolution.com

11/9/2010

2

Normal Probability Distribution

However, the EXACT

probability of a

particular value from

a Normal

Distribution is

ZERO.

e.g. P(X=140) = 0

P=95 140

Normal Probability Distribution

b

a

What information do we need to calculate P(a x b)?

The normal probability distribution

is defined by the equation

linereal the on x all or

e

21

1

=f(x)

2

1

-x

2

1

-¸

¸

¹

·

¨

¨

©

§

Normal Probability Distribution

b

a

What information do we need to calculate P(a x b)?

Pand V

Normal Probability Distribution

b

a

To calculateTo calculate

P(a x b):P(a x b):

Pand V

Normal

Random

Variable

X= “measured”

e.g. X= a person’s weight

Parameters

Presentation of Solution

Follow the “normal” template – page 269

X = ____________________

For example: X= number of .... WRONG

1=

µ = Normal

P ( ) = P ( X symbol # ) = Ncd ( L, U, 1, µ ) = 0.xxxx

(words) ( <, >, , ) 4 decimals

Must draw a diagram

(Mean, 1, value, shading)

Suppose that the weights of adults are normally distributed

with a mean of 170.0lbs and a standard deviation of 25.0

lbs.

What is the probability that a person weighs from 150 to

190 lbs?

V= 25.0

Note:

Calculating “normal” probability =

Finding area under a portion

of the normal curve

P=170 190

150

X= a person’s weight

P= 170.0 lbs

V= 25.0 lbs

P( 150 x 190) = Ncd (150,190, 25, 170)

Lower upper VP

Refer to the calculator Lesson 5:

Page 169

normal

www.notesolution.com

11/9/2010

3

Normal Probability Exercises

Page 269 to 270

Q6.1 to Q6.6

Inverse Normal

Normal Probability Distribution

Given the value X, find

the probability (or

the area under the

)

The Inverse Normal

Probability means:

Given the probability

curve

)

(area), find the x

value?

What

is the

area?

Given X µ

1

Area=

0.3

X=? µ

1

Inverse Normal Probability

The weights of adults are normally distributed with a mean of 170.0 lbs

and a standard deviation of 25.0 lbs.

1) What is the maximum weight of the lightest 30% of the population?

Present your solution as follows(use the template)

X = person’s weight

P= 170.0

V= 25.0

P( X

d

?)

=

0.30

Area= V= 25.0

Normal

P(

X

d

?

)

0.30

? = =

CASIO Calculator: select STATmode F5 (DIST) F1 (NORM) F3 (InvN)

X = InvN(0.3, 25, 170) =

Written statement: The lightest 30% weigh at most 156.9 lbs

0.3

X=?P= 170.0

»

»

»

¼

º

«

«

«

¬

ª

P

V

Area

Inv

Inverse Normal Probability

The weights of adults are normally distributed with a mean of 170.0 lbs

and a standard deviation of 25.0 lbs.

2) What is the minimum weight to be in the heaviest 30% of the

population? Present your solution as follows(use the template)

X = person’s weight

P= 170.0

V= 25.0

P( X

?) 030

V= 25.0

NormalArea = 0.3

P(

X

?

)

=

0

.

30

? = =

CASIO Calculator: select STATmode F5 (DIST) F1 (NORM) F3 (InvN)

X = InvN((1-0.3), 25, 170) = InvN(0.7, 25, 170)

Written statement: The heaviest 30% weigh at least 183.1 lbs.

X=?

P= 170.0

»

»

»

¼

º

«

«

«

¬

ª

P

V

Area

Inv

NOTE

When using the InvN function,

the Area value that is required is

the area tothe

LEFT

of the

the

area

to

the

LEFT

of

the

desired X value.

Area=

0.3

Area=

0.7

www.notesolution.com

Over 90% improved by at least one letter grade.

OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A!

Leah — University of Toronto

Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be.

Saarim — University of Michigan

As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes.

Jenna — University of Wisconsin

OneClass has allowed me to catch up with my most difficult course! #lifesaver

Anne — University of California

Join OneClass

Access over 10 million pages of study

documents for 1.3 million courses.

Sign up

Join to view

OR

By registering, I agree to the
Terms
and
Privacy Policies

Already have an account?
Log in

Just a few more details

So we can recommend you notes for your school.

Reset Password

Please enter below the email address you registered with and we will send you a link to reset your password.

Add your courses

Get notes from the top students in your class.