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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.

Formula:  normdist(x2, mn, sd, 1) - normdist(x1, mn, sd, 1)

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