# Statistics - Z-table

The Z-distribution is a standardized normal distribution where the mean is 0 and the standard deviation is 1.

The Z-distribution can be used to find which percent of a population is within a particular number of standard deviations.

## Z-Distribution and Table for Negative Z-values

The numbers in the table cells correspond to the area under the graph.

The area under graph is the probability of getting a value that is smaller than z.

The probabilities are decimal values and can be thought of as percentages. For example: 0.1515 is 15.15%.

z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
-3.40.00030.00030.00030.00030.00030.00030.00030.00030.00030.0002
-3.30.00050.00050.00050.00040.00040.00040.00040.00040.00040.0003
-3.20.00070.00070.00060.00060.00060.00060.00060.00050.00050.0005
-3.10.00100.00090.00090.00090.00080.00080.00080.00080.00070.0007
-3.00.00130.00130.00130.00120.00120.00110.00110.00110.00100.0010
-2.90.00190.00180.00180.00170.00160.00160.00150.00150.00140.0014
-2.80.00260.00250.00240.00230.00230.00220.00210.00210.00200.0019
-2.70.00350.00340.00330.00320.00310.00300.00290.00280.00270.0026
-2.60.00470.00450.00440.00430.00410.00400.00390.00380.00370.0036
-2.50.00620.00600.00590.00570.00550.00540.00520.00510.00490.0048
-2.40.00820.00800.00780.00750.00730.00710.00690.00680.00660.0064
-2.30.01070.01040.01020.00990.00960.00940.00910.00890.00870.0084
-2.20.01390.01360.01320.01290.01250.01220.01190.01160.01130.0110
-2.10.01790.01740.01700.01660.01620.01580.01540.01500.01460.0143
-2.00.02280.02220.02170.02120.02070.02020.01970.01920.01880.0183
-1.90.02870.02810.02740.02680.02620.02560.02500.02440.02390.0233
-1.80.03590.03510.03440.03360.03290.03220.03140.03070.03010.0294
-1.70.04460.04360.04270.04180.04090.04010.03920.03840.03750.0367
-1.60.05480.05370.05260.05160.05050.04950.04850.04750.04650.0455
-1.50.06680.06550.06430.06300.06180.06060.05940.05820.05710.0559
-1.40.08080.07930.07780.07640.07490.07350.07210.07080.06940.0681
-1.30.09680.09510.09340.09180.09010.08850.08690.08530.08380.0823
-1.20.11510.11310.11120.10930.10750.10560.10380.10200.10030.0985
-1.10.13570.13350.13140.12920.12710.12510.12300.12100.11900.1170
-1.00.15870.15620.15390.15150.14920.14690.14460.14230.14010.1379
-0.90.18410.18140.17880.17620.17360.17110.16850.16600.16350.1611
-0.80.21190.20900.20610.20330.20050.19770.19490.19220.18940.1867
-0.70.24200.23890.23580.23270.22960.22660.22360.22060.21770.2148
-0.60.27430.27090.26760.26430.26110.25780.25460.25140.24830.2451
-0.50.30850.30500.30150.29810.29460.29120.28770.28430.28100.2776
-0.40.34460.34090.33720.33360.33000.32640.32280.31920.31560.3121
-0.30.38210.37830.37450.37070.36690.36320.35940.35570.35200.3483
-0.20.42070.41680.41290.40900.40520.40130.39740.39360.38970.3859
-0.10.46020.45620.45220.44830.44430.44040.43640.43250.42860.4247
-0.00.50000.49600.49200.48800.48400.48010.47610.47210.46810.4641

## Z-Distribution and Table of Positive Z-Values

The numbers in the table cells correspond to the area under the graph.

The area under graph is the probability of getting a value that is smaller than z.

The probabilities are decimal values and can be thought of as percentages. For example: 0.7088 is 70.88%.

z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.00.50000.50400.50800.51200.51600.51990.52390.52790.53190.5359
0.10.53980.54380.54780.55170.55570.55960.56360.56750.57140.5753
0.20.57930.58320.58710.59100.59480.59870.60260.60640.61030.6141
0.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.6517
0.40.65540.65910.66280.66640.67000.67360.67720.68080.68440.6879
0.50.69150.69500.69850.70190.70540.70880.71230.71570.71900.7224
0.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.7549
0.70.75800.76110.76420.76730.77040.77340.77640.77940.78230.7852
0.80.78810.79100.79390.79670.79950.80230.80510.80780.81060.8133
0.90.81590.81860.82120.82380.82640.82890.83150.83400.83650.8389
1.00.84130.84380.84610.84850.85080.85310.85540.85770.85990.8621
1.10.86430.86650.86860.87080.87290.87490.87700.87900.88100.8830
1.20.88490.88690.88880.89070.89250.89440.89620.89800.89970.9015
1.30.90320.90490.90660.90820.90990.91150.91310.91470.91620.9177
1.40.91920.92070.92220.92360.92510.92650.92790.92920.93060.9319
1.50.93320.93450.93570.93700.93820.93940.94060.94180.94290.9441
1.60.94520.94630.94740.94840.94950.95050.95150.95250.95350.9545
1.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.9633
1.80.96410.96490.96560.96640.96710.96780.96860.96930.96990.9706
1.90.97130.97190.97260.97320.97380.97440.97500.97560.97610.9767
2.00.97720.97780.97830.97880.97930.97980.98030.98080.98120.9817
2.10.98210.98260.98300.98340.98380.98420.98460.98500.98540.9857
2.20.98610.98640.98680.98710.98750.98780.98810.98840.98870.9890
2.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.9916
2.40.99180.99200.99220.99250.99270.99290.99310.99320.99340.9936
2.50.99380.99400.99410.99430.99450.99460.99480.99490.99510.9952
2.60.99530.99550.99560.99570.99590.99600.99610.99620.99630.9964
2.70.99650.99660.99670.99680.99690.99700.99710.99720.99730.9974
2.80.99740.99750.99760.99770.99770.99780.99790.99790.99800.9981
2.90.99810.99820.99820.99830.99840.99840.99850.99850.99860.9986
3.00.99870.99870.99870.99880.99880.99890.99890.99890.99900.9990
3.10.99900.99910.99910.99910.99920.99920.99920.99920.99930.9993
3.20.99930.99930.99940.99940.99940.99940.99940.99950.99950.9995
3.30.99950.99950.99950.99960.99960.99960.99960.99960.99960.9997
3.40.99970.99970.99970.99970.99970.99970.99970.99970.99970.9998

## Example of How to Use the Z-Table

The Z-value is found combining the numbers in the first column and the first row.

For example, the probability for getting a z-value smaller than 1.85 is found by finding the number in the table where the row is 1.8 and the column is 0.05.

So the probability is: 0.9678 is 96.78%.

z .00 .01 .02 .03 .04 .05 .06 .07 .08 .09
0.00.50000.50400.50800.51200.51600.51990.52390.52790.53190.5359
0.10.53980.54380.54780.55170.55570.55960.56360.56750.57140.5753
0.20.57930.58320.58710.59100.59480.59870.60260.60640.61030.6141
0.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.6517
0.40.65540.65910.66280.66640.67000.67360.67720.68080.68440.6879
0.50.69150.69500.69850.70190.70540.70880.71230.71570.71900.7224
0.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.7549
0.70.75800.76110.76420.76730.77040.77340.77640.77940.78230.7852
0.80.78810.79100.79390.79670.79950.80230.80510.80780.81060.8133
0.90.81590.81860.82120.82380.82640.82890.83150.83400.83650.8389
1.00.84130.84380.84610.84850.85080.85310.85540.85770.85990.8621
1.10.86430.86650.86860.87080.87290.87490.87700.87900.88100.8830
1.20.88490.88690.88880.89070.89250.89440.89620.89800.89970.9015
1.30.90320.90490.90660.90820.90990.91150.91310.91470.91620.9177
1.40.91920.92070.92220.92360.92510.92650.92790.92920.93060.9319
1.50.93320.93450.93570.93700.93820.93940.94060.94180.94290.9441
1.60.94520.94630.94740.94840.94950.95050.95150.95250.95350.9545
1.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.9633
1.80.96410.96490.96560.96640.96710.96780.96860.96930.96990.9706
1.90.97130.97190.97260.97320.97380.97440.97500.97560.97610.9767
2.00.97720.97780.97830.97880.97930.97980.98030.98080.98120.9817
2.10.98210.98260.98300.98340.98380.98420.98460.98500.98540.9857
2.20.98610.98640.98680.98710.98750.98780.98810.98840.98870.9890
2.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.9916
2.40.99180.99200.99220.99250.99270.99290.99310.99320.99340.9936
2.50.99380.99400.99410.99430.99450.99460.99480.99490.99510.9952
2.60.99530.99550.99560.99570.99590.99600.99610.99620.99630.9964
2.70.99650.99660.99670.99680.99690.99700.99710.99720.99730.9974
2.80.99740.99750.99760.99770.99770.99780.99790.99790.99800.9981
2.90.99810.99820.99820.99830.99840.99840.99850.99850.99860.9986
3.00.99870.99870.99870.99880.99880.99890.99890.99890.99900.9990
3.10.99900.99910.99910.99910.99920.99920.99920.99920.99930.9993
3.20.99930.99930.99940.99940.99940.99940.99940.99950.99950.9995
3.30.99950.99950.99950.99960.99960.99960.99960.99960.99960.9997
3.40.99970.99970.99970.99970.99970.99970.99970.99970.99970.9998

W3Schools is optimized for learning and training. Examples might be simplified to improve reading and learning. Tutorials, references, and examples are constantly reviewed to avoid errors, but we cannot warrant full correctness of all content. While using W3Schools, you agree to have read and accepted our terms of use, cookie and privacy policy.