Download Z Table and Discover Its Applications in Statistics

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Aug 8, 2023
9 min read

How to Download a Z-Table

A z-table, also known as a standard normal table, is a useful tool for finding probabilities associated with z-scores in a normal distribution. A z-score, also called a standard score, is a measure of how many standard deviations a value is away from the mean. By converting any normal distribution to a standard normal distribution with mean 0 and standard deviation 1, you can use a z-table to find the area under the curve to the left or right of any z-score. This area represents the probability of getting a value less than or greater than the z-score.

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In this article, you will learn about the different types of z-tables and how to read them, where to find z-tables online and in books, how to download a z-table as a PDF or Excel file, and how to create your own z-table in Excel or Google Sheets.

Types of Z-Tables and How to Read Them

There are at least three different conventions for z-tables, depending on what kind of probability you want to find:

Cumulative from mean: This type of z-table gives the probability that a z-score is between 0 (the mean) and a given value. For example, if you look up 0.25 in this table, you will get 0.2549, which means that there is a 25.49% chance that a z-score is between 0 and 0.25.

Cumulative: This type of z-table gives the probability that a z-score is less than or equal to a given value. For example, if you look up 0.25 in this table, you will get 0.7549, which means that there is a 75.49% chance that a z-score is less than or equal to 0.25.

Complementary cumulative: This type of z-table gives the probability that a z-score is greater than or equal to a given value. For example, if you look up 0.25 in this table, you will get 0.2451, which means that there is a 24.51% chance that a z-score is greater than or equal to 0.25.

To use any type of z-table, you need to first calculate the z-score for the value you are interested in using the formula:

where x is the value, μ is the mean, and σ is the standard deviation.

Then, you need to find the row that matches the integer part and the first decimal place of the z-score, and the column that matches the second decimal place of the z-score. The value in the table cell is the probability corresponding to the table type.

For example, suppose you want to find the probability that a value from a normal distribution with mean 50 and standard deviation 10 is less than or equal to 55 using a cumulative z-table. First, you need to calculate the z-score for 55:

Then, you need to look up 0.50 in the cumulative z-table:

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You will see that the value in the table cell is 0.6915, which means that there is a 69.15% chance that a value from the normal distribution is less than or equal to 55.

Sources of Z-Tables Online and in Books

If you don't want to create your own z-table, you can find many sources of z-tables online and in books. Here are some examples:

: This website provides interactive z-tables for all three types of probabilities, as well as a z-score calculator and a normal distribution graph.

: This website provides a cumulative z-table with explanations and examples of how to use it.

: This website provides a complementary cumulative z-table with explanations and examples of how to use it.

: This website provides a cumulative from mean z-table with explanations and examples of how to use it.

: This book by William DeCoursey provides a cumulative z-table in Appendix A.

: This book by David Moore, William Notz, and Michael Fligner provides a cumulative z-table in Appendix B.

How to Download a Z-Table as a PDF or Excel File

If you want to download a z-table as a PDF or Excel file, you can use one of the following methods:

Method 1: Save the web page as a PDF or Excel file: If you find a z-table online that you like, you can save the web page as a PDF or Excel file by using the print function of your browser. For example, in Google Chrome, you can click on the three dots icon in the top right corner, select Print, and then choose Save as PDF or Microsoft Excel as the destination. You can then name and save the file to your computer.

Method 2: Copy and paste the table into a PDF or Excel file: If you find a z-table online that you like, you can copy and paste the table into a PDF or Excel file by using the keyboard shortcuts Ctrl+C and Ctrl+V (or Command+C and Command+V on Mac). You can then format the table as you wish and save the file to your computer.

Method 3: Download the table from a source that provides it as a PDF or Excel file: Some sources of z-tables online provide them as PDF or Excel files that you can download directly. For example, provides a complementary cumulative z-table as an Excel file. You can simply click on the link and save the file to your computer.

How to Create Your Own Z-Table in Excel or Google Sheets

If you want to create your own z-table in Excel or Google Sheets, you can use the following steps:

Create a blank spreadsheet: Open Excel or Google Sheets and create a new blank spreadsheet.

Label the rows and columns: In the first row, enter 0.00, 0.01, 0.02, ..., 0.09 in cells B1 to K1. These are the second decimal places of the z-scores. In the first column, enter 0.0, 0.1, 0.2, ..., 3.9 in cells A2 to A40. These are the integer parts and the first decimal places of the z-scores.

Enter the formula for the probability: In cell B2, enter the formula =NORM.DIST(A2+B1,0,1,FALSE) for Excel or =NORMDIST(A2+B1,0,1,FALSE) for Google Sheets. This formula calculates the probability that a z-score is less than or equal to the value in cell A2+B1 using the standard normal distribution with mean 0 and standard deviation 1. The FALSE argument indicates that we want the probability density function, not the cumulative distribution function.

Copy and paste the formula to fill the table: Select cell B2 and drag it to cell K40 to copy and paste the formula to fill the table. You should see the probabilities corresponding to each z-score in each cell.

Format the table as you wish: You can format the table as you wish by changing the font size, color, alignment, borders, etc. You can also add a title and a header to the table.

You have now created your own z-table in Excel or Google Sheets. You can use it to find probabilities for any z-score by looking up the corresponding cell value.

Conclusion

A z-table is a handy tool for finding probabilities associated with z-scores in a normal distribution. You can use different types of z-tables depending on what kind of probability you want to find. You can also find z-tables online and in books, download them as PDF or Excel files, or create your own z-table in Excel or Google Sheets. By using a z-table, you can simplify the process of calculating probabilities and make your statistical analysis easier and faster.

If you want to learn more about z-tables and how to use them, you can check out the following resources:

: This article explains what a z-score is and how to calculate it.

: This article shows how to use the z-table to find probabilities for different scenarios.

: This article provides some practice problems with solutions for using the z-table.

FAQs

What is the difference between a positive and a negative z-table?

A positive z-table gives the probabilities for positive z-scores, while a negative z-table gives the probabilities for negative z-scores. You can use either table by using the symmetry property of the normal distribution, which states that the probability of getting a value above or below the mean is the same. For example, if you want to find the probability of getting a z-score less than -0.25, you can look up 0.25 in the positive z-table and get 0.7549, which is the same as looking up -0.25 in the negative z-table.

How can I find the area between two z-scores using a z-table?

To find the area between two z-scores using a z-table, you need to subtract the smaller probability from the larger probability. For example, if you want to find the area between -1 and 1 using a cumulative z-table, you need to look up 1 and get 0.8413, and look up -1 and get 0.1587. Then, you need to subtract 0.1587 from 0.8413 and get 0.6826, which is the area between -1 and 1.

What are some common applications of z-tables in statistics?

Z-tables are commonly used in statistics for various purposes, such as:

Hypothesis testing: Z-tables can help you determine whether to reject or fail to reject a null hypothesis based on a test statistic and a significance level.

Confidence intervals: Z-tables can help you calculate the margin of error and the confidence interval for a population mean or proportion based on a sample mean or proportion and a confidence level.

Standardization: Z-tables can help you compare values from different normal distributions by converting them to standard scores.

How can I check the accuracy of my z-table calculations?

To check the accuracy of your z-table calculations, you can use one of the following methods:

Use an online calculator: You can use an online calculator that can perform z-score and probability calculations for you. For example, can help you find probabilities for any type of z-score using a standard normal distribution.

Use a graphing tool: You can use a graphing tool that can plot a normal distribution curve and show you the area under the curve for any range of values. For example, can help you visualize probabilities for any type of z-score using a standard normal distribution.

Use an inverse function: You can use an inverse function that can find the z-score for a given probability or vice versa. For example, in Excel or Google Sheets, you can use the NORM.INV function or the NORMSINV function to find the z-score for a given probability using a standard normal distribution.

What are some alternatives to z -tables for finding probabilities?

Z-tables are not the only way to find probabilities for normal distributions. Some alternatives to z-tables are:

T-tables: T-tables are similar to z-tables, but they are used for finding probabilities for t-scores, which are based on the Student's t-distribution. The Student's t-distribution is a family of distributions that are similar to the normal distribution, but have more variability and thicker tails. T-tables are often used when the sample size is small or the population standard deviation is unknown.

Calculator functions: Many calculators have built-in functions that can find probabilities for normal distributions and other distributions. For example, in a TI-84 calculator, you can use the normalcdf function to find the probability of getting a value between two z-scores, or the invNorm function to find the z-score for a given probability.

Software programs: Many software programs, such as Excel, Google Sheets, R, Python, SPSS, etc., have functions or packages that can find probabilities for normal distributions and other distributions. For example, in Excel or Google Sheets, you can use the NORM.DIST function or the NORMDIST function to find the probability of getting a value less than or equal to a z-score, or the NORM.S.DIST function or the NORMSDIST function to find the probability of getting a value greater than or equal to a z-score.

I hope this article has helped you understand how to download a z-table and how to use it for finding probabilities. If you have any questions or feedback, please leave a comment below. Thank you for reading!

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