Z-Table

Are you taking a Statistics class?

This application is going to save you a lot of time!

Write the value of Z or the probability and get the result with one click.

Forget the paper table and use your Android phone!!!!!!!!!

New Version:
- Added right,middle,left and two tail.
- Calculate Z given the probability

Normal Distribution Calculator
Z-Table Examples

1 - Find the area under the standard normal curve:

a) P(Z = 1.45)

b) P(Z = -1.21)

c) P(Z > 1.45)

d) P(Z < -1.21)

e) P(Z < 1.45)

f) P(Z > -1.21)

g) P( -1.21 < Z < 1.45)

h) P( 1.33 < Z < 2.12)

i) P( -2.12 < Z < -1.33)

j) P( -1.21 < Z and Z > 1.45)

2 - Find the Z value(s) knowing that the area under the standard normal curve is:

a) P = 0.4265 (Between 0 and ±Z)

b) P = 0.3869 (Between 0 and ±Z)

c) P = 0.0735 (Greater than Z)

e) P = 0.9265 (Less than Z)

f) P = 0.8869 (Greater than Z)

g) P = 0.8530 (Between Z and -Z)

h) P = 0.2262 (Less than -Z and greater than Z)

a) P(Z = 1.45)

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

P(Z = 1.45) = 0.4265

Using the Z-Table application:

P(Z = 1.45) = 0.4265

-> Return examples list

b) P(Z = -1.21)

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177

P(Z = -1.21) = 0.3869

Using the Z-Table application:

P(Z = -1.21) = 0.3869

-> Return examples list

c) P(Z > 1.45)

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

P(Z > 1.45) = 0.5 - 0.4265 = 0.0735

Using the Z-Table application:

P(Z > 1.45) = 0.0735

-> Return examples list

d) P(Z < -1.21)

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177

P(Z < -1.21) = 0.5 - 0.3869 = 0.1131

Using the Z-Table application:

P(Z < -1.21) = 0.1131

-> Return examples list

e) P(Z < 1.45)

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

P(Z < 1.45) = 0.5+0.4265 = 0.9265

Using the Z-Table application:

P(Z < 1.45) = 0.4265

-> Return examples list

f) P(Z > -1.21)

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177

P(Z > -1.21) = 0.5+0.3869 = 0.8869

Using the Z-Table application:

P(Z > -1.21) = 0.8869

-> Return examples list

g) P(-1.21 < Z < 1.45)

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

P(-1.21 < Z < 1.45) = 0.3869 + 0.4265 = 0.8134

Using the Z-Table application:

P(-1.21 < Z < 1.45) = 0.8134

-> Return examples list

h) P(1.33 < Z < 2.12)

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
... ... ... ... ... ... .... ... ... ... ...
2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857
2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890

P(1.33 < Z < 2.12) = 0.4830 - 0.4082 = 0.0748

Using the Z-Table application:

P(1.33 < Z < 2.12) = 0.0748

-> Return examples list

i) P( -2.12 < Z < -1.33 )

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
... ... ... ... ... ... .... ... ... ... ...
2.0 0.4772 0.4778 0.4783 0.4788 0.4793 0.4798 0.4803 0.4808 0.4812 0.4817
2.1 0.4821 0.4826 0.4830 0.4834 0.4838 0.4842 0.4846 0.4850 0.4854 0.4857
2.2 0.4861 0.4864 0.4868 0.4871 0.4875 0.4878 0.4881 0.4884 0.4887 0.4890

P( -2.12 < Z < -1.33 ) = 0.4830 - 0.4082 = 0.0748

Using the Z-Table application:

P(-2.12 < Z < -1.33) = 0.0748

-> Return examples list

j) P(-1.21 < Z and Z > 1.45)

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

P(-1.21 < Z and Z > 1.45) = 1- (0.3869 + 0.4265) = 0.1866

Using the Z-Table application:

P(-1.21 < Z and Z > 1.45) = 0.1866

-> Return examples list

a) P = 0.4265 (Between 0 and ±Z)

or

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

Z = ±1.45

Using the Z-Table application:

Z = ±1.45

-> Return examples list

b) P = 0.3869 (Between 0 and ±Z)

or

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177

Z = ±1.21

Using the Z-Table application:

Z = ±1.21

-> Return examples list

c) P = 0.0735 (Greater than Z)

The probability value is less than 0.5. It tells us the Z value is positive.

We need to look for 0.5 - 0.0735 = 0.4265 inside the table because the probabilities are based on the area beween 0 and Z.

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

Z > 1.45

Using the Z-Table application:

Z > 1.45

-> Return examples list

d) P = 0.1131 (Less than Z)

The probability value is less than 0.5. It tells us the Z value is negative.

We need to look for 0.5 - 0.1131 = 0.3869 inside the table because the probabilities are based on the area beween 0 and Z.

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177

Z < -1.21

Using the Z-Table application:

Z < -1.21

-> Return examples list

e) P = 0.9265 (Less than Z)

The probability value is greater than 0.5. It tells us the Z value is positive.

We need to look for 0.9265 - 0.5 = 0.4265 inside the table because the probabilities are based on the area beween 0 and Z.

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

Z < 1.45

Using the Z-Table application:

Z < 1.45

-> Return examples list

f) P = 0.8869 (Greater than Z)

The probability value is greater than 0.5. It tells us the Z value is negative.

We need to look for 0.8869 - 0.5 = 0.3869 inside the table because the probabilities are based on the area beween 0 and Z.

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177

Z > -1.21

Using the Z-Table application:

Z > -1.21

-> Return examples list

g) P = 0.8530 (Between Z and -Z)

We need to look for 0.8530/2 = 0.4265 inside the table because the probabilities are based on the area beween 0 and Z.

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177
1.4 0.4192 0.4207 0.4222 0.4236 0.4251 0.4265 0.4279 0.4292 0.4306 0.4319
1.5 0.4332 0.4345 0.4357 0.4370 0.4382 0.4394 0.4406 0.4418 0.4429 0.4441

-1.45 < Z < 1.45

Using the Z-Table application:

-1.45 < Z < 1.45

-> Return examples list

h) P = 0.2262 (Less than -Z and greater than Z)

We need to look for (1 - 0.2262) / 2 = 0.3869 inside the table because the probabilities are based on the area beween 0 and Z.

Using the paper table:

Standard Normal (Z) Table (Area between 0 and z)
0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1.1 0.3643 0.3665 0.3686 0.3708 0.3729 0.3749 0.3770 0.3790 0.3810 0.3830
1.2 0.3849 0.3869 0.3888 0.3907 0.3925 0.3944 0.3962 0.3980 0.3997 0.4015
1.3 0.4032 0.4049 0.4066 0.4082 0.4099 0.4115 0.4131 0.4147 0.4162 0.4177