The Manga Guide to Statistics

There is a

certain way to

describe this

in statistics.

Remember...

The phrase sms so

complicated.

"X foows what with

what and what"...?!

That is beyond my

comprehension.

We, it does

sound rather

peculiar, but just

remember that's

the way it goes.

Let's return to

the story about

the test.

If the probability

density function

of "english test

results" is like

this...

When the formula for probability density function of X is

You say that “X foows a normal distribution with mean

μ and standard deviation σ .”

Normal distribution with mean 53 and standard deviation 10

ƒ(x) =

1

√2�(standard deviation of x)

e

−

1

2

( )

x − mean of x

standard deviation of x

2

88 Chapter 5

When the formula for probability density function of x is

You don't say, "x Foows a normal distribution with mean 0

and standard deviation 1." In statistics, we describe this as a

standard normal distribution.

You can say the results of the

english test foow a normal

distribution with mean 53 and

standard deviation 10.

I think I am

starting to

get it!

Now, for the

next topic.

3. Standard Normal Distribution

Yes, sir.

ƒ(x) =

1

√2�(standard deviation of x)

e

−

1

2

( )

x − mean of x

standard deviation of x

2

=

1

√2�1 ×

e

−

1

2

( )

x − 0

1

2

=

1

√2�

e

−

1

2

x

2

Let's Obtain the Probability 89

...!?

Again, let's use that

English test as an

example.

Suose "english test results"

foows the normal distribution

with mean 53 and standard

deviation 10.

OK.

z-score of

Test Results

mean

standard deviation

each value - mean

standard deviation

Then, "English test results" after

standardization would...

Student Score

1

2

10,421

Foow the standard

normal distribution.

We standardized the

"English Test results"

data.

Standard Normal Distribution

Wow, that

lks

familiar!

Don't give up!

The goal is close!

What is our

goal, anyway?

Let's Obtain the Probability 91

Z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

0.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.0359

0.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.0753

0.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.1064 0.1103 0.1141

1.8 0.4641 0.4649 0.4656 0.4664 0.4671 0.4678 0.4686 0.4693 0.4699 0.4706

1.9 0.4713 0.4719 0.4726 0.4732 0.4738 0.4744 0.4750 0.4756 0.4761 0.4767

... ... ... ... ... ... ... ... ... ... ...

... ... ... ... ... ... ... ... ... ... ...

Wake up, Rui!

Shake,

shake!

Table of Standard Normal Distribution

This table

tes you the

area of this

part under

the graph.

What? Area?

What do you

mean?

T many numbers...

RECOVERY!

Ah, you are

alive!

92 Chapter 5