How to use the normal distribution interval probability calculator
Find the probability that a normally distributed value lies between two bounds. Enter mean μ, standard deviation σ, lower bound, upper bound in the fields above; the probability between bounds, probability above upper bound are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “normal probability between two values”, “probability within range normal”, “bell curve area between”, “calculate normal distribution interval probability”, “find probability between bounds”.
Formula
Variables
- mu — Mean μ
- sigma — Standard deviation σ
- a — Lower bound
- b — Upper bound
Worked example
With mean μ = 100, standard deviation σ = 15, lower bound = 85, upper bound = 115, the calculator gives probability between bounds ≈ 68.26895 %; probability above upper bound ≈ 15.86553 %.
Frequently asked questions
What is the normal distribution interval probability calculator used for?
Find the probability that a normally distributed value lies between two bounds. It helps with questions such as “normal probability between two values”, “probability within range normal”, “bell curve area between”.
What is the formula for the normal distribution interval probability calculation?
Probability between bounds (%) = 100 × (ncdf((b-mu) / sigma)-ncdf((a-mu) / sigma)). Probability above upper bound (%) = 100 × (1-ncdf((b-mu) / sigma)). Here mu is mean μ, sigma is standard deviation σ, a is lower bound, b is upper bound.
What inputs do I need for the normal distribution interval probability calculator?
You need mean μ, standard deviation σ, lower bound, upper bound. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the normal distribution interval probability calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the normal distribution interval probability result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.