This interactive Z table displays probabilities (areas) under the standard normal distribution curve for specific z-scores. It helps determine the probability of values falling within particular ranges in normally distributed data. Hover over any table value to visualize the corresponding shaded area in the distribution chart along with its exact probability. You can also click on any value to pin it and maintain the shaded area visualization for closer examination.
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
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
1 - pnorm(1.25)
# or
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
Understanding Z Scores and the Normal Distribution
What is a Z Score?
A z-score (also called a standard score) measures how many standard deviations an observation is from the mean. The formula is:
z = (x - μ) / σZ Score Calculator
To calculate a z-score, you need the value (x), population mean (μ), and standard deviation (σ).
Standard Normal Distribution
The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.