Q-Norm Calculator

Calculate the quantile of a normal distribution given probability, mean, and standard deviation.

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About This Tool

This qnorm calculator computes the quantile (inverse cumulative distribution function) of a normal distribution. Input a probability value (between 0 and 1), mean, and standard deviation to find the corresponding z-score or x-value. Supports left, right, and two-tailed calculations for statistical analysis and hypothesis testing. The tool uses precise mathematical algorithms to ensure accurate results for educational, research, and professional use.

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How to Use

Enter a probability value between 0 and 1 in the 'Probability' field.
Enter the mean (default is 0 for standard normal).
Enter the standard deviation (default is 1 for standard normal).
Select the tail type: Left-tailed (probability in left tail), Right-tailed (probability in right tail), or Two-tailed (probability split between both tails).
Click 'Calculate Quantile' to compute the result.
View the quantile value, z-score, and explanation in the results section.

Frequently Asked Questions

Find Quick Answers

What is a qnorm calculator?

A qnorm calculator computes the quantile (inverse cumulative distribution function) of a normal distribution. Given a probability, it returns the corresponding value on the distribution curve.

What is the difference between left-tailed and right-tailed?

Left-tailed calculates the quantile where the probability is in the left tail (e.g., probability = 0.05 gives a negative z-score). Right-tailed calculates where the probability is in the right tail (e.g., probability = 0.05 gives a positive z-score). Two-tailed splits the probability equally between both tails.

Can I use this for standard normal distribution?

Yes, by setting mean = 0 and standard deviation = 1, the calculator returns the z-score. For other normal distributions, adjust mean and standard deviation accordingly.

What if I get an error?

Ensure probability is between 0 and 1, standard deviation is positive, and all fields are filled. The tool will highlight invalid inputs and display specific error messages.

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