Student Z Distribution Table, Appendix B: Use Of Statistical Tables

Use the negative Z score table below to find values on the left of the mean as can be seen in the graph alongside. Corresponding values which are less than the mean are marked with a negative score in the z-table and respresent the area under the bell curve to the left of z.

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(Note that this method of mapping the Z Score value is same for both the positive as well as the negative Z Scores. That is because for a standard normal distribution table, both halfs of the curves on the either side of the mean are identical. So it only depends on whether the Z Score Value is positive or negative or whether we are looking up the area on the left of the mean or on the right of the mean when it comes to choosing the respective table)

Why are there two Z tables?

There are two Z tables to make things less complicated. Sure it can be combined into one single larger Z-table but that can be a bit overwhelming for a lot of beginners and it also increases the chance of human errors during calculations. Using two Z tables makes life easier such that based on whether you want the know the area from the mean for a positive value or a negative value, you can use the respective Z score table.

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If you want to know the area between the mean and a negative value you will use the first table (1.1) shown above which is the left-hand/negative Z-table. If you want to know the area between the mean and a positive value you will the second table (1.2) above which is the right-hand/positive Z-table.

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What is Standard Deviation? (σ)

Standard Deviation denoted by the symbol (σ) , the greek letter for sigma, is nothing but the square root of the Variance. Whereas Variance is average of the squared differences from the Mean.

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Sample Questions For Practice 

1. What is P (Z ≥ 1.20)

Answer: 0.11507

To find out the answer using the above Z-table, we will first look at the corresponding value for the first two digits on the Y axis which is 1.2 and then go to the X axis for find the value for the second decimal which is 0.00. Hence we get the score as 0.11507

2. What is P (Z ≤ 1.20)

(Same as above using the other table. Try solving this yourself for practice)

Answer: 0.88493

History of Standard Normal Distribution Table

The credit for the discovery, origin and penning down the Standard Normal Distribution can be attributed to the 16th century French mathematician Abraham de Moivre ( 26th May 1667 – 27th November 1754) who is well known for his ‘de Moivre’s formula’ which links complex numbers and trigonometry.

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