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Normal Distribution CDF for 2 Values Calculator

Calculates the cumulative distribution function between two values.

distribution image

The cumulative normal distribution function between x1 and x2.

See the Statistical Distributions Overview page for more statistical distribution calculators.

Example 1

A baseball shall weigh not less than five nor more than 5 1/4 ounces avoirdupois.

If a shipment has an mean of 5.1 oz and standard deviation of .05 oz, what percent are within the specifications

Value Keystrokes Display Description
5 x1 5.0000 Stores the x1 value.
5.25 x2 5.2500 Stores the x2 value.
5.1 μ 5.100 Stores the mn (mean) value.
.05 σ 0.0500 Stores the sd (standard deviation) value.
  cdf 0.9759 Calculates the cumulative normal distribution between x1 and x2.

So, about 97.6%

Example 2

What would the standard deviation of be so that 99% are within the specifications?

These keystrokes assume the values from example 1.

Value Keystrokes Display Description
.99 cdf .9900 Stores the cdf value.
  σ 0.0428 Calculates the sd value.


Normal distribution - Wikipedia