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Normal Distribution CDF for 2 Tails Calculator

Calculates the 2 tail cumulative normal distribution function.

distribution image

The 2 tail cumulative normal distribution function.

Formula: 1 - (1 - normdist(x, mn, sd, 1)) * 2

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 mn of 5 1/8 oz and sd of .1 oz, what percent are within the specifications

Value Keystrokes Display Description
5.25 x 5.2500 Stores the x value.
5.125 μ 5.1250 Stores the mn (mean) value.
.1 σ 0.1000 Stores the sd (standard deviation) value.
  cdf 0.7887 Calculates the cumulative distribution between -x and +x.

So, about 75%

Example 2

What should 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 0.0485 Calculates the sd value.


Normal distribution - Wikipedia