TATITIC CALCULATOR
Normal Distribution
A precise tool.
What is the Normal Distribution & How does it work?
The normal distribution, also known as the Gaussian curve, describes how values of a random variable are distributed around a mean.
It is symmetric, bellβshaped, and fully defined by its mean (ΞΌ) and standard deviation (Ο), which control location and spread.
Statisticians use the Zβscore to translate any normal variable into the standard normal form, enabling probability lookup.
f(x) = frac{1}{sigmasqrt{2pi}} e^{-frac{(x-mu)^2}{2sigma^2}}
ΞΌ = mean, Ο = standard deviation
Parameters
Result
β
Frequently Asked Questions
How do I calculate the probability of a value in a normal distribution?
To find the probability, input your mean (ΞΌ) and standard deviation (Ο), then enter the value. The calculator will give you the area under the curve to the left of that value.
What is a Z-score in a normal distribution?
A Z-score tells how many standard deviations an element is from the mean. It’s calculated as (x – ΞΌ) / Ο, where x is your data point.
How do I find the Z-score for a given probability?
Input your desired probability and the calculator will return the corresponding Z-score that cuts off that area under the curve.
Can this calculator handle non-standard normal distributions?
Yes, you can input any mean (ΞΌ) and standard deviation (Ο) to calculate probabilities for a normal distribution with those parameters.
What does the bell-shaped curve represent in a normal distribution?
The bell-shaped curve represents the probability density function of a normal distribution, showing how data is distributed around the mean.
How do I interpret the results from this calculator?
The results will give you probabilities or Z-scores. Probabilities represent the likelihood of a value occurring within a certain range, while Z-scores indicate how far a value is from the mean in terms of standard deviations.
Is there a limit to the number of calculations I can perform?
No, you can use this calculator for as many calculations as needed without any limitations.
Results are for informational purposes only and do not constitute professional advice.