Statistics For Dummies
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You can use the z-table to find a full set of "less-than" probabilities for a wide range of z-values. To use the z-table to find probabilities for a statistical sample with a standard normal (Z-) distribution, follow the steps below.

Using the Z-table

  1. Go to the row that represents the ones digit and the first digit after the decimal point (the tenths digit) of your z-value.

  2. Go to the column that represents the second digit after the decimal point (the hundredths digit) of your z-value.

  3. Intersect the row and column from Steps 1 and 2.

    This result represents p(Z < z), the probability that the random variable Z is less than the value Z (also known as the percentage of z-values that are less than the given z-value ).

For example, suppose you want to find p(Z < 2.13). Using the z-table below, find the row for 2.1 and the column for 0.03. Intersect that row and column to find the probability: 0.9834. Therefore p(Z < 2.13) = 0.9834.

z-score table 1
z-score table 2

Noting that the total area under any normal curve (including the standardized normal curve) is 1, it follows that p(Z < 2.13) + p(Z > 2.13) =1. Therefore, p(Z > 2.13) = 1 – p(Z < 2.13) which equals 1 – 0.9834 which equals 0.0166.

Symmetry in the distribution

Suppose you want to look for p(Z < –2.13). You find the row for –2.1 and the column for 0.03. Intersect the row and column and you find 0.0166; that means p(Z < –2.13)=0.0166. Observe that this happens to equal p(Z>+2.13). The reason for this is because the normal distribution is symmetric. So the tail of the curve below –2.13 representing p(Z < –2.13) looks exactly like the tail above 2.13 representing p(Z > +2.13).

About This Article

This article is from the book:

About the book author:

Deborah J. Rumsey, PhD, is an Auxiliary Professor and Statistics Education Specialist at The Ohio State University. She is the author of Statistics For Dummies, Statistics II For Dummies, Statistics Workbook For Dummies, and Probability For Dummies.

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