Z Table Calculator

The Z Table Calculator allows users to input a Z-Score and a specified direction (left-tailed, right-tailed, or two-tailed) to calculate and display the corresponding probability, percentile, area under the curve, and confidence level.

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How to Use the Z Table Calculator

This step-by-step guide will help you to effectively use the Z Table Calculator to find probabilities, percentiles, area under the curve, and confidence levels based on a given Z-Score.

Step 1: Input Your Z-Score

Begin by locating the input field labeled Z-Score. Enter a numerical value, ensuring it falls within the range of -4.0 to 4.0. This value should be entered to two decimal places (e.g., 1.96).

Step 2: Select the Direction

Next, move to the input field labeled Direction. This field is a dropdown menu with three options to specify the tail of interest:

  • Left-tailed (less than): Calculates the probability that a value is less than the given Z-Score.
  • Right-tailed (greater than): Calculates the probability that a value is greater than the given Z-Score.
  • Two-tailed (both sides): Considers the extreme values on both sides of the distribution and calculates the combined probability.

Select the direction that best suits your analysis purpose. This selection is mandatory for the calculation process.

Step 3: Review and Understand the Results

Upon entering your Z-Score and selecting the direction, the calculator will provide four result fields:

  • Probability: This result shows the probability corresponding to your inputted Z-Score based on the error function. It is formatted to four decimal places.
  • Percentile: Displays the percentile rank corresponding to the Z-Score. This is shown as a percentage formatted to two decimal places.
  • Area Under the Curve: Indicates the area under the normal distribution curve. This is particularly insightful for understanding the distribution coverage for the specified tail. It is formatted to four decimal places.
  • Confidence Level: Provides the confidence level percentage for the selected direction, and is formatted to two decimal places. For a two-tailed selection, it reflects the confidence that the observed data falls within this range.

Conclusion

By following the above steps, you can successfully calculate and interpret the results produced by the Z Table Calculator. Whether you are conducting a statistical analysis or working on an academic project, this tool provides comprehensive insights into Z-Score data. Always ensure your inputs are accurate for valid results.