The Z-table, also known as the standard normal distribution table or Z-score table, is a statistical tool used to find the probability that a random variable with a standard normal distribution will fall within a specified range. The Z-table is essential in hypothesis testing, confidence intervals, and other statistical analyses.
What is a Z-Table?
A Z-table is a table that shows the area under the standard normal curve to the left of a given Z-score. The Z-score is a measure of how many standard deviations an element is from the mean. The Z-table is typically arranged with Z-scores ranging from -3 to 3, with increments of 0.01.
How to Read a Z-Table:
To read a Z-table, you need to understand the following:
- Z-score: The Z-score is the number of standard deviations from the mean. A positive Z-score indicates that the value is above the mean, while a negative Z-score indicates that the value is below the mean.
- Area to the left: The area to the left of the Z-score represents the probability that a random variable with a standard normal distribution will be less than or equal to the given Z-score.
- Table values: The table values represent the area to the left of the Z-score. For example, if the Z-score is 1.23, the table value would give you the area to the left of 1.23, which is approximately 0.8907.
Z-Table Pdf:
Here is a sample Z-table pdf:
| Z-score | Area to the left |
|---|---|
| -3.00 | 0.0013 |
| -2.99 | 0.0014 |
| -2.98 | 0.0015 |
| … | … |
| -1.23 | 0.1093 |
| -1.22 | 0.1112 |
| -1.21 | 0.1131 |
| … | … |
| 0.00 | 0.5000 |
| 0.01 | 0.5040 |
| 0.02 | 0.5080 |
| … | … |
| 1.23 | 0.8907 |
| 1.24 | 0.8925 |
| 1.25 | 0.8943 |
| … | … |
| 3.00 | 0.9987 |
Key Takeaways:
- Z-tables are essential: Z-tables are crucial in statistical analysis, particularly in hypothesis testing and confidence intervals.
- Understanding Z-scores: Z-scores measure the number of standard deviations from the mean, helping you understand the probability of a value occurring.
- Reading the Z-table: The Z-table provides the area to the left of a given Z-score, representing the probability that a random variable will be less than or equal to the given Z-score.
Frequently Asked Questions:
- What is the difference between a Z-table and a T-table? A Z-table is used for large sample sizes (n > 30), while a T-table is used for small sample sizes (n < 30).
- How do I calculate a Z-score? The Z-score is calculated using the formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
- What is the significance of a Z-score of 1.96? A Z-score of 1.96 corresponds to a probability of 0.975, indicating that 95% of the values lie within 1.96 standard deviations of the mean.
What is the purpose of a Z-table in statistics?
+The Z-table is used to find the probability that a random variable with a standard normal distribution will fall within a specified range, which is essential in hypothesis testing, confidence intervals, and other statistical analyses.
How do I interpret the values in a Z-table?
+The values in a Z-table represent the area to the left of the Z-score, which corresponds to the probability that a random variable will be less than or equal to the given Z-score.
What is the difference between a Z-table and a standard normal distribution curve?
+A Z-table is a tabular representation of the standard normal distribution curve, providing the area to the left of a given Z-score. The standard normal distribution curve, on the other hand, is a graphical representation of the distribution, showing the probability density function.
By understanding how to read and interpret a Z-table, you can apply this knowledge to solve problems in statistics, hypothesis testing, and confidence intervals.
