Math Calculators, Lessons and Formulas

It is time to solve your math problem

mathportal.org

# Normal distribution calculator

Enter mean, standard deviation and cutoff points and this calculator will find the area under normal distribution curve. The calculator will generate a step by step explanation along with the graphic representation of the area you want to find.

Normal Distribution Calculator
Find the area under normal distribution curve
show help ↓↓ examples ↓↓
0123456789-del

If $X$ is a normally distributed variable with mean $\mu =$ and standard deviation $\sigma =$ find one of the following probabilities:

Hide steps
working...
examples
example 1:ex 1:
A normally distributed random variable $X$ has a mean of $20$ and a standard deviation of $4$. Determine the probability that a randomly selected x-value is between $15$ and $22$.
example 2:ex 2:
The final exam scores in a statistics class were normally distributed with a mean of $58$ and a standard deviation of $4$. Find the probability that a randomly selected student scored more than $62$ on the exam.
example 3:ex 3:
The target inside diameter is $50 \, \text{mm}$ but records show that the diameters follows a normal distribution with mean $50 \, \text{mm}$ and standard deviation $0.05 \, \text{mm}$. An acceptable diameter is one within the range $49.9 \, \text{mm}$ to $50.1 \, \text{mm}$. What proportion of the output is acceptable?

Quick Calculator Search