Standard Normal Table - Wikipedia

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Formatting / layout

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Z tables are typically composed as follows:

  • The label for rows contains the integer part and the first decimal place of Z.
  • The label for columns contains the second decimal place of Z.
  • The values within the table are the probabilities corresponding to the table type. These probabilities are calculations of the area under the normal curve from the starting point (0 for cumulative from mean, negative infinity for cumulative and positive infinity for complementary cumulative) to Z.

Example: To find 0.69, one would look down the rows to find 0.6 and then across the columns to 0.09 which would yield a probability of 0.25490 for a cumulative from mean table or 0.75490 from a cumulative table.

To find a negative value such as –0.83, one could use a cumulative table for negative z-values[3] which yield a probability of 0.20327.

But since the normal distribution curve is symmetrical, probabilities for only positive values of Z are typically given. The user might have to use a complementary operation on the absolute value of Z, as in the example below.

Types of tables

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Z tables use at least three different conventions:

Cumulative from mean gives a probability that a statistic is between 0 (mean) and Z. Example: Prob(0 ≤ Z ≤ 0.69) = 0.2549. Cumulative gives a probability that a statistic is less than Z. This equates to the area of the distribution below Z. Example: Prob(Z ≤ 0.69) = 0.7549. Complementary cumulative gives a probability that a statistic is greater than Z. This equates to the area of the distribution above Z. Example: Find Prob(Z ≥ 0.69). Since this is the portion of the area above Z, the proportion that is greater than Z is found by subtracting Z from 1. That is Prob(Z ≥ 0.69) = 1 − Prob(Z ≤ 0.69) or Prob(Z ≥ 0.69) = 1 − 0.7549 = 0.2451.

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