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Calculate z-scores, cumulative probability, tail probability, and interval probability for a normal distribution
Execution
Fill in the form, run the tool, and review the result in one place.
Samples
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Tool usage guide
The Normal Distribution Calculator allows you to perform statistical analysis by calculating z-scores, cumulative probabilities, and interval probabilities based on your specific mean and standard deviation parameters.
Background
An exam has a mean score of 75 with a standard deviation of 10.
Problem
Determine how a score of 85 compares to the rest of the class.
How to use
Input 85 as the raw value, 75 as the mean, and 10 as the standard deviation.
rawValue: 85, meanInput: 75, standardDeviationInput: 10Outcome
The calculator returns a z-score of 1 and a cumulative probability of 0.8413, indicating the score is in the 84th percentile.
Background
A machine produces parts with a mean length of 100mm and a standard deviation of 15mm.
Problem
Find the probability that a part length is between 85mm and 115mm.
How to use
Input 100 as the mean, 15 as the standard deviation, and set the lower bound to 85 and upper bound to 115.
meanInput: 100, standardDeviationInput: 15, lowerBound: 85, upperBound: 115A z-score represents the number of standard deviations a data point is from the mean of the distribution.
It measures the probability that a random variable will take a value less than or equal to the specified raw value.
Yes, by entering values into the Lower Bound and Upper Bound fields, the tool calculates the probability of a value falling within that range.
The tool defaults to 4 decimal places, but you can adjust this between 0 and 10 based on your needs.
No, this calculator is specifically designed for data that follows a normal (Gaussian) distribution.
Outcome
The tool calculates an interval probability of 0.6827, showing that approximately 68.27% of parts fall within this range.