1. About the Two Different Standard Normal (Z) Tables
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2. Two Tables, same answer.
You will see two different types of Z Tables. Some textbooks use one, some use the other, some include both for reference and give you a choice.
It is best to become familiar enough to use both types of Z tables. This will help you to better understand using normal probabilities and making inferences using the standard normal distribution.
The Two Z Tables

3. The “0 to z” Standard Normal Distribution Table
Areas Between 0 and a Z-value
The Two Z Tables

4. Normal Distribution
Source: Levine et al, Business Statistics, Pearson.
The Two Z Tables

5. Example: Weight
If the weight of males is N.D. with μ=150 and σ=10, what is the probability that a randomly selected male will weigh between 140 lbs and 155 lbs?
[Important Note: Always remember that the probability that X is equal to any one particular value is zero, P(X=value) =0, since the normal distribution is continuous.] 
The Two Z Tables

6. Example: Weight Solution: Z = (140 – 150)/ 10 = -1.00 s.d. from mean
Z = (140 – 150)/ 10 = s.d. from mean
Area under the curve = (from Z table)
Z = (155 – 150) / 10 =+.50 s.d. from mean
Area under the curve = (from Z table)
Answer: = .5328
The Two Z Tables

7. The Cumulative Standard Normal Distribution Table
Areas Between -∞ and a Z-value
The Two Z Tables

8. Cumulative Standard Normal Table
The Two Z Tables

9. Cumulative Z-Table
The cumulative Z-Table provides the area underneath the curve from -∞ to a specific Z value.
The other Z-table we used, shows areas between 0 and Z.
A Z-score of 0.00 will place you at the 50th percentile. A positive Z-score means you are above the 50th percentile and a negative Z-score means you are below the 50th percentile.
Note that there are two Cumulative Standard Normal Distribution tables, one for negative Z scores and one for positive Z scores. In either case, you are finding the area between -∞ and a specific Z score.
The Two Z Tables

10. Using the Cumulative Z-Table
For example, if we want to know the area between -∞ and -1.70, we can find that directly from the Cumulative Z Table, which tells us that it is
Alternatively, since the “0 to Z” Table shows the area between 0 and a z value, we note that the area between 0 and (same as the area between 0 and +1.70) is Thus, the area under the Z distribution between -∞ and is =
The Two Z Tables

11. Cumulative Z-Table: Percentiles
You can easily use the Cumulative Z Table to determine percentiles of the normal distribution. For example,
Suppose that your grade on a standardized test (whose scores follows a normal distribution) converts to a Z-score of From the table, the probability of getting a score between -∞ and is Approximately 29.81% of the scores are lower than yours. In effect, you are almost at the 30th percentile.
Using the 0-to-Z table, the area between 0 and (which is the same as the area between 0 and -0.53) is For the percentile, =
Say your Z-score on the standardized test is This converts to a cumulative normal probability of This means that the area between -∞ and is about 96% and your score puts you at approximately the 96th percentile.
Using the 0-to-Z table, the area between 0 and is .4599; add the area between -∞ and which is and you get
The Two Z Tables

12. Cumulative Z-Table: Examples
Example 1: If your score on a standardized test that follows a normal distribution is +2.17, you are at which percentile? Answer: .985 or 98.5%. Only 1.5% of people taking the test get better scores. Example 2: If your score on a standardized test that follows a normal distribution is -1.34, you are at which percentile? Answer: or 9.01% % of people taking the test get better scores.
The Two Z Tables