Normal Distribution Calculator
Many measurements, such as heights, test scores and measurement errors, follow a normal distribution. Enter the mean and standard deviation to find probabilities.
From a probability to a value
How to use it
- Type the mean and the standard deviation.
- Type a value x, or two values for a range, to get the probabilities.
- To go the other way, type a probability and choose the tail.
Frequently asked questions
What is the 68-95-99.7 rule?
In a normal distribution, about 68.27% of values fall within one standard deviation of the mean, 95.45% within two and 99.73% within three.
How accurate are the results?
The cumulative distribution is computed with a series and a continued fraction, accurate to about 13 significant digits even far in the tails, and checked against Python's statistics library.
Which value covers 95% in the middle?
The central 95% lies between μ − 1.96σ and μ + 1.96σ. Choose central interval in the second part of the calculator to get the limits for any probability.
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