Z table | Z Score Table

Z Table is a type of statistical table. It is also known as the standard normal table or Z score table. Also, some people calling it a unit normal table. Read this article to know various things related to the Z score table.

Negative Z Table

Negative Z Table

Positive Z Table

Positive Z Table

Z table, an alphabetical term in the world of mathematics has its interesting origins from history. A French mathematician Abraham de Moivre was interested in gambling and used to find probabilities of the coin flips. So, he devised a bell-shaped figure on the graph which we usually call the z curve. Z table is simply a standard normal distribution of percentage from 1 to 100. It reflects the area of the z curve on the graph for standard deviations. For instance, the variables of height, weight, and strength can be shown by this standard distribution. This phenomenon was first considered by Lambert Quetelet. A Belgian astronomer, he linked this distribution and the z curve.

The z table has numerous values. It is using to find the probability of a statistic value as in where it lies. Whether above, below, or between the values of normal distribution. Remember, the z- score shows the number of standard deviations where the value lies below the mean. It is positive when it lies above the mean. The question here arises as to where are there two z tables separately. Since we have two values which are positive and negative, so this approach makes our better understanding as well as the solution to the problem. The left denotes the negative values and the right shows the positive values.

Usage of Z score table

Conversion to a z-score:

The formula to convert a sample mean, X, to a z-score is:

z score formula

Here μ is the population mean, σ is the population standard deviation, and x is the sample size.

Area corresponding to z-score:

After this calculation, you need to look up in the table. Don’t get confused with the right and left side of the mean.

Sketch a conclusion with a diagram:

The area below the z curve is the one that needs to be calculated. It means that the shaded portion below the curve is the answer and it gives you a better idea of the figures.

The three convocations:

  1. The cumulative, from the mean that it provides a statistic value between 0 and Z.
  2. The cumulative, that provides a statistical value less than Z or the area of below the distribution.
  3. The complementary cumulative, which provides a figure more than Z. It is equal to the area of the distribution above Z.

Let us understand this concept with an example:

Example 1:

The distribution of test scores has a mean of 80 and a standard deviation of 5.2. State the percentage of score that lies below 73.


According to the question,
The area below the z curve starts from the left side of the graph.

73 as z score:
z = 73 – (80 / 5.2) = 1.34615

Now, you can trace the value in the z table and that will take you to the percentage of the score of -1.34.

Example 2:

The normal curve shows mean as 0 and the standard deviation is 1. Let us assume that the area within is 1.45 standard deviation above the mean. The shaded portion is 0.4265.


In order to find the area of 0.4265, we have to read across the table of 0.5.

1.4 + 0.05 = 1.45 standard deviation

So, the area shown through 1.45 standard deviation is the shaded one in the standard normal curve. It is above the mean.

Advantages of Z score table

  • It plays a significant role in comparing the raw figures of the data. The tests which are taken from the data at interval management are traced by the z score table.
  • The z score table is a crystal clear table as in its reliability and credibility. You can easily trace the right value.
  • We have got several figures. So, through this z score table, we can easily compare the values of different aspects. The comparison doesn’t require any hard code formula just a wise insight on the table.

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