2 Z Tables and how to use them correctly

The Standard Normal Table is also commonly know as the Z table. It is used in the calculation of probability on the LEFT side of the normal distribution. To use the Table Calculate the Z value using the formula:

Z value formula for Z table

Understanding the table

When looking at a Z table we should first focus on the LEFT COLUMN and TOP ROW. The left column has the Z value up to the first decimal and the Top row has the second decimal of the Z value. For example, If you have a Z value of 2.34, then 2.3 will be in the left column and 0.04 will be in top row. The probability associated with 2.34 will be at the intersection of these values. In this case probability of the Z value 2.34 will be 0.9904 from the Z table. This is the area under the curve of the Normal Distribution on the LEFT side of the given Z value.

Negative Z table

The Standard Normal Distribution has a mean of 0 and a standard deviation of 1. This makes the range of the Z values from -3.99 to +3.99. The table is thus divided in two parts. from -3.99 to 0 and 0 to 3.99. The part of the table from -3.99 to 0 is called as the Negative Z table and should be used when the calculated Z value is negative. The Negative Z table is given below.

Negative Z table

Positive Z Table

Use the Positive table when the calculated Z value is between 0 and +3.99. The table is given below.

Positive Z table

Practice with Z table

To become familiar with using a Z table find the probability values of the following Z values.

  1. 2.68
  2. 1.94
  3. – 0.08
  4. – 2.71
  5. – 1.64
  6. 2.30
  7. 1.23
  8. -2.22
  9. 0.67
  10. 2.00

The probability values that we get from the Z table for the above examples are as follows

  1. 0.9963 by using the positive table
  2. 0.9738 by using the positive table
  3. 0.4681 by using the negative table
  4. 0.0034 by using the negative table
  5. 0.0505 by using the negative table
  6. 0.9893 by using the positive table
  7. 0.8907 by using the positive table
  8. 0.0132 by using the negative table
  9. 0.7486 by using the positive table
  10. 0.9772 by using the positive table

The Z table is used for solving problems on normal distribution. Learn more about the Normal Distribution Here.

You can find some solved examples of normal distribution problems with Z table here.

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