Home  
  Z-Table  
  EngEco  
  Contact Us  
 



 
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

Z-Table
Normal Distribution Calculator
(Click here to buy)
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)

d) P = 0.1131 (Less 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)

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

Answer:

P(Z = 1.45) = 0.4265

Using the Z-Table application:

z-table z=1.45

Answer:

P(Z = 1.45) = 0.4265

-> Return examples list

b) P(Z = -1.21)

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

Answer:

P(Z = -1.21) = 0.3869

Using the Z-Table application:

z-table z<-1.21

Answer:

P(Z = -1.21) = 0.3869

-> Return examples list

c) P(Z > 1.45)

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

Answer:

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

Using the Z-Table application:

z-table z>1.45

Answer:

P(Z > 1.45) = 0.0735

-> Return examples list


d) P(Z < -1.21)

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

Answer:

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

Using the Z-Table application:

z-table z<-1.21

Answer:

P(Z < -1.21) = 0.1131

-> Return examples list

e) P(Z < 1.45)

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

Answer:

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

Using the Z-Table application:

z-table z<1.45

Answer:

P(Z < 1.45) = 0.4265

-> Return examples list

f) P(Z > -1.21)

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

Answer:

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

Using the Z-Table application:

z-table z>-1.21

Answer:

P(Z > -1.21) = 0.8869

-> Return examples list

g) P(-1.21 < Z < 1.45)

-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

Answer:

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

Using the Z-Table application:

z-table -1.21<z<1.45

Answer:

P(-1.21 < Z < 1.45) = 0.8134

-> Return examples list


h) P(1.33 < Z < 2.12)

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

Answer:

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

Using the Z-Table application:

z-table 1.33 < z <-2.12

Answer:

P(1.33 < Z < 2.12) = 0.0748

-> Return examples list

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

-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

Answer:

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

Using the Z-Table application:

z-table -2.13<z<1.33

Answer:

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

-> Return examples list


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

-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

Answer:

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

Using the Z-Table application:

z-table -1.21<z and x>1.45

Answer:

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

-> Return examples list

a) P = 0.4265 (Between 0 and ±Z)

z = 1.45    or     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

Answer:

Z = ±1.45

Using the Z-Table application:

Probability= 0.4265 (Between 0 and ±Z)

Answer:

Z = ±1.45

-> Return examples list

b) P = 0.3869 (Between 0 and ±Z)

z = -1.21    or     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

Answer:

Z = ±1.21

Using the Z-Table application:

Probability = 0.3869 (Between 0 and ±Z)

Answer:

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.

z > 1.45

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

Answer:

Z > 1.45

Using the Z-Table application:

Probability = 0.0735 (Greater than Z)

Answer:

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.

z<-1.21

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

Answer:

Z < -1.21

Using the Z-Table application:

Probability = 0.1131 (Less than Z)

Answer:

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.

z < 1.45

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

Answer:

Z < 1.45

Using the Z-Table application:

Probability = 0.9265 (Less than Z)

Answer:

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.

z>-1.21

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

Answer:

Z > -1.21

Using the Z-Table application:

Probability = 0.8869 (Greater than Z)

Answer:

Z > -1.21

-> Return examples list

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

-1.45 < z < 1.45

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

Answer:

-1.45 < Z < 1.45

Using the Z-Table application:

Probability = 0.8530 (Between Z and -Z)

Answer:

-1.45 < Z < 1.45

-> Return examples list


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

z<-1.21 and z >1.21

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

Answer:

-1.21 < Z < 1.21

Using the Z-Table application:

Probability = 0.2262 (Less than -Z and greater than Z)

Answer:

-1.21 < Z < 1.21

-> Return examples list

If you have any questions or recommendations do not hesitate to contact us: carpediemeng@gmail.com Thanks!