Z-Score Table

Last Updated : 7 Jul, 2026

A Z-score table helps you find the probability of a value in a standard normal distribution. It shows how much area lies to the left of a particular z-value. The distribution is bell-shaped with a mean 0 and standard deviation 1.

  • The rows and columns of the table define the z-score, and the table cells represent the area.
  • For example, the z-score 1.50 corresponds to the area 0.9332, which is the probability that a random variable from a standard normal distribution will fall below 1.50.
standard_normal_distribution

Note: The negative z-scores are below the mean, while the positive z-scores are above the mean.

The z-score table is divided into two sections:

1. Positive Z-Score Table: A data point is above the median if its Z-score is positive (greater than 0), with a higher value denoting a larger divergence from the mean.

2. Negative Z-Score Table: A negative Z-score indicates that the data points are nearer the mean.

How to Use a Z-Score Table

Step 1: Calculate the Z-score: Use the formula to find how many standard deviations X is from the mean.

Step 2: Open the Z-score table: Z-values appear up to two decimals (0.00, 0.01, 0.02, ...).

Step 3: Locate the Z-score: Find the row for the first decimal and the column for the second decimal.

The table value gives P(Z ≤ z).

Example: A school has a normally distributed test score with a mean (μ) of 75 and a standard deviation (σ) of 10. A student wants to know the probability of scoring less than 80 on a test.

Solution:

Calculate the Z-score:

Z = 80 −75/10
⇒ Z = 0.5

Look at the Z-scores in the Z-score table to find the corresponding cumulative probability. Let’s say 0.6915.

Thus, the probability of a student scoring less than 80 would be 0.6915 or 69.15%.

How to Interpret Z-Score

  • Positive z-score -> value is above the mean. Example: Z = 2 -> 2 standard deviations above the mean.
  • Negative z-score -> value is below the mean. Example: Z = −1.5 -> 1.5 standard deviations below the mean.

Applications of Z Score

Z-scores are widely used in many areas, such as:

  • Comparing data in statistics and detecting outliers
  • Financial analysis (e.g., Altman Z-score for bankruptcy prediction)
  • Medical and growth assessments using reference charts
  • Performance comparison in sports and academics
  • Hypothesis testing, confidence intervals and general data analysis

➣Practice: Solved Examples

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