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Ciprian Cristea
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Download Z Table PDF: A Complete Guide to the Standard Normal Distribution


How to Download Z Table PDF




If you are studying statistics, you might have encountered the term "z table" or "standard normal table". A z table is a useful tool that helps you find the probability of certain values occurring in a normal distribution. In this article, you will learn what a z table is, why you need it, how to use it, and where to find it in PDF format.




download z table pdf



What is a Z Table?




A z table, also known as the standard normal table, is a mathematical table that shows the values of Φ, the cumulative distribution function of the standard normal distribution. The standard normal distribution, denoted by Z, is a special case of the normal distribution where the mean is 0 and the standard deviation is 1.


A z table is used to find the probability that a statistic (such as a sample mean or a test score) is observed below, above, or between certain values on the standard normal distribution. By extension, it can also be used to find probabilities for any normal distribution, as long as you convert its values into z scores first.


There are different types of z tables, depending on how they show the probabilities. The most common ones are:


  • Cumulative from mean: This type of z table gives the probability that a statistic is between 0 (the mean) and Z. For example, if you look up 0.69 in this table, you will get 0.2549, which means that there is a 25.49% chance that a statistic is between 0 and 0.69 standard deviations away from the mean.



  • Cumulative: This type of z table gives the probability that a statistic is less than Z. This equates to the area under the curve to the left of Z. For example, if you look up 0.69 in this table, you will get 0.7549, which means that there is a 75.49% chance that a statistic is less than 0.69 standard deviations away from the mean.



  • Complementary cumulative: This type of z table gives the probability that a statistic is greater than Z. This equates to the area under the curve to the right of Z. For example, if you look up 0.69 in this table, you will get 0.2451, which means that there is a 24.51% chance that a statistic is greater than 0.69 standard deviations away from the mean.



Why Do You Need a Z Table?




A z table has many advantages for statistics students and researchers. Some of them are:


  • It simplifies calculations: A z table allows you to easily find probabilities for any value on the standard normal distribution without having to use complex formulas or calculators.



  • It standardizes data: A z table helps you compare data sets with different means and standard deviations by converting them into standard scores (z scores) that have a common scale.



  • It has many applications : A z table is useful for many statistical concepts and methods, such as confidence intervals, hypothesis testing, correlation, regression, and more. It can help you answer questions such as: How likely is it that a sample mean is within a certain range of the population mean? How significant is the difference between two proportions? How strong is the relationship between two variables?



Here are some examples of how z tables are used in real life:


  • Education: Teachers and students can use z tables to analyze test scores and grades. For example, a teacher can use a z table to find out what percentage of students scored above or below the class average, or what score corresponds to a certain percentile rank.



  • Psychology: Psychologists and researchers can use z tables to measure and compare human traits and behaviors. For example, a psychologist can use a z table to find out how common or rare a certain IQ score is, or how likely it is that a person has a certain personality type.



  • Business: Business owners and managers can use z tables to make decisions and predictions based on data. For example, a business owner can use a z table to estimate the demand for a new product, or the probability of making a profit or loss.



How to Use a Z Table?




To use a z table, you need to follow these steps:


  • Standardize your data: If your data follows a normal distribution with any mean and standard deviation, you need to convert it into z scores using the formula: z = (x - μ) / σ, where x is the value you want to find the probability for, μ is the mean of the distribution, and σ is the standard deviation of the distribution. This will transform your data into a standard normal distribution with mean 0 and standard deviation 1.



  • Find your z score: If your data is already in z scores, you can skip this step. Otherwise, you need to find the z score that corresponds to the value you are interested in. For example, if you want to find the probability that a test score is less than 75, and the test scores follow a normal distribution with mean 70 and standard deviation 10, you need to find the z score for 75 using the formula: z = (75 - 70) / 10 = 0.5.



  • Read the z table: Depending on the type of probability you want to find, you need to choose the appropriate z table (cumulative from mean, cumulative, or complementary cumulative) and look up your z score in it. The z table will give you two digits for the row and two digits for the column. The row corresponds to the first digit and the first decimal place of your z score, while the column corresponds to the second decimal place of your z score. For example, if your z score is 0.5, you need to look at the row for 0.5 and the column for 0.00. The value at the intersection of the row and column is the probability you are looking for. For example, if you are using a cumulative z table, the probability for 0.5 is 0.6915.



Here is an example of how to use a z table step by step:


Suppose you want to find the probability that a person has an IQ score between 90 and 110, given that IQ scores follow a normal distribution with mean 100 and standard deviation 15.


  • Standardize your data: To convert 90 and 110 into z scores, use the formula: z = (x - μ) / σ, where x is 90 or 110, μ is 100, and σ is 15. This gives you: z = (90 - 100) / 15 = -0.67 for 90, and z = (110 - 100) / 15 = 0.67 for 110.



  • Find your z scores: You already have your z scores from step 1: -0.67 and 0.67.



  • Read the z table: To find the probability that a person has an IQ score between 90 and 110, you need to find the area under the curve between -0.67 and 0.67 on the standard normal distribution. This means you need to use a cumulative from mean z table and subtract the probabilities for -0.67 and 0.



Using a cumulative from mean z table, you can find the probabilities for -0.67 and 0 as follows:


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Z


0.00


0.01


0.02


0.03


...


0.0


0.0000


0.0039


0.0078


0.0117


...


-0.6


0.1915


0.1877


0.1839


0.1801


...


-0.7


0.2549


0.2514


0.2478


0.2443


...


...


...


...


...


...


...


The probability for -0.67 is at the intersection of the row for -0.6 and the column for 0.07, which is 0.1877. The probability for 0 is a


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