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# Calculators :: Statistics Calculators :: 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

Enter mean, standard deviation and cutoff points in order to find the area under normal curve. Important: The form will NOT let you enter wrong characters (like y, p, ;, ...)

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

 $P~($ $~< X <$ $~)$ $P~(X>$ $)$ $P~( X <$ $~~)$
Show me an explanation.

## How to use this calculator

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.

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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.

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Example 3:

The target inside diameter is 50 mm but records show that the diameters follows a normal distribution with mean 50 mm and standard deviation 0.05 mm. An acceptable diameter is one within the range 49.9 mm to 50.1 mm. What proportion of the output is acceptable?

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