Cola izquierda
Less than
Adds all probability to the left of a boundary.
Probability and Statistics
Normal distribution and Z-score calculator
Locate values, calculate areas under the normal curve or find the value corresponding to a percentile.
What do you want to calculate?
Choose a question and work with original X values or directly with Z.
Publicidad
How to read the normal curve
The same distribution can answer different questions depending on the shaded area.
Cola derecha
Greater than
Measures the proportion above a boundary.
Central area
Between two values
Subtracts the cumulative probabilities at the upper and lower boundaries.
Dos colas
Outside the interval
Adds the regions below and above the two boundaries.
What the Z-score represents
The Z-score converts any normal distribution to a scale with mean 0 and standard deviation 1. This lets you compare values measured in different units.
z = (x − mean) / standard deviation
Supuesto importante
The calculator assumes that the variable follows a normal distribution. It does not test normality or determine whether a result is good, bad or clinically relevant.
Frequently asked questions
What is a Z-score?
A Z-score indicates how many standard deviations a value is from the mean. A positive Z is above the mean and a negative Z is below it.
How do you interpret a positive or negative Z-score?
The sign indicates the side of the mean. The magnitude indicates distance: Z = 1.5 means 1.5 standard deviations above it; Z = -1.5 means the same distance below it.
What does percentile mean?
The percentile approximates the percentage of the distribution to the left of a value. The 90th percentile leaves about 90% of values below it.
How do I calculate the probability below or above a value?
Choose Calculate probability, select Less than or Greater than, and enter the boundary. If you are using X values, add the mean and standard deviation.
How do I calculate the probability between two values?
Select Between and enter a lower and upper boundary. The calculator subtracts the cumulative probabilities at the two boundaries.
How do I find a value from a percentile?
Choose Find a value, enter the percentile and, when using X, the mean and standard deviation. The critical Z is calculated first and then converted to the original scale.
What is the difference between less than and less than or equal to?
In a continuous distribution, the probability of one exact value is zero. Therefore, less than and less than or equal to produce the same probability.
Does the calculator verify that my data follows a normal distribution?
No. The tool calculates results under a normal-distribution assumption, but it does not run a normality test on your data.