The interactive Z table shows probabilities (areas) under the standard normal distribution curve for given z-scores. It is used to find the probability of a value falling within a specific range in a normally distributed dataset.
How to Use the Z Table
- Find the z-score's ones digit and first decimal place in the leftmost column
- Find the second decimal place in the top row
- The intersection gives you the probability
- Hover over any value to see the shaded area in the distribution chart
Examples of Using the Z Table
Example 1: Z = 1.84
- Locate 1.8 in the left column
- Find 0.04 in the top row
- The intersection gives 0.9671, meaning P(Z < 1.84) = 0.9671
- P(Z > 1.84) = 1 - P(Z < 1.84) = 1 - 0.9671 = 0.0329
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pnorm(1.84)Example 2: Z = -1.25
There are two ways to calculate P(Z < z) for negative z-scores:
- Simply choose the negative z-scores tab on the table above and locate the z-score
- Symmetry property: P(Z < z) = 1 - P(Z < z)
Let's use the symmetry property for this example:
- Use the symmetry property: P(Z < -1.25) = 1 - P(Z < 1.25)
- Find P(Z < 1.25) in the table: 0.8944
- Calculate: P(Z < -1.25) = 1 - 0.8944 = 0.1056
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1 - pnorm(1.25)
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pnorm(-1.25)Pro Tip:
- For P(Z > a), calculate 1 - P(Z < a)
- For P(a < Z < b), calculate P(Z < b) - P(Z < a)
- Remember that the total area under the curve equals 1