How to Use a Z-Score Table?

To use the Z Score Table, use the following steps:

• Step 1: Determine the Z-score associated with the relevant data point. Verify that you possess the distribution’s mean (μ) and standard deviation (σ). The number of standard deviations that a data point deviates from the mean is shown by the Z-score.
• Step 2: Look for a normal distribution table or a Z-score table. Z-scores are usually shown in the left column of these tables, with matching probabilities or percentiles shown in the table’s body.
• Step 3: Look for the Z-score you determined in the table’s left column. Two decimal places are frequently used when listing Z-scores (e.g., 0.00, 0.01, 0.02, etc.). Calculate the likelihood by interpolating between the two closest values if your Z-score is not exactly listed.

Note: The chance of getting a result less than or equal to the one you computed is represented by the corresponding value in the table.

Let’s consider an example for better understanding.

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%.

Z Score Table is the table for determining the probability of a standard normal variable falling below or above a certain value. Z-score table, also known as a standard normal table or z-score Table, is a mathematical table that provides the area under the curve to the left of a z-score in a standard normal distribution. The standard normal distribution is a bell-shaped curve with a mean of 0 and a standard deviation of 1.

The z-score table is used to find the probability that a random variable from a standard normal distribution will fall below a certain value. In this article, we will learn about the Z Score Table in sufficient detail and also learn how to use the Z Score Table in numerical problems.