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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

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

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examples
example 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:
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:
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?

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