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Normal Distribution CDF for 2 Tails Calculator

This CDF calculator computes the cumulative probability P(μ-x <= X <= μ+x) for a given normal distribution and also offers features including inverse CDF calculations, and solving for the mean (μ) and standard deviation (σ). It can also create a plot as a function of any of the paramaters.

CDF2Tails

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

Example 1

Determine the likelihood that the actual revenue will closely align with the forecasted figure, falling within a $0.5 million range above or below the $10 million forecast, with historical deviations suggesting a standard deviation of $1 million.. This analysis will help gauge the forecast's reliability, supporting more informed business decisions and strategic adjustments as needed.

Value Keystrokes Display Description
.5 x 0.500 Stores the x value.
10 μ 10.0 Stores the μ (mean) value.
1 σ 1.00 Stores the σ (standard deviation) value.
  P(μ±x) 0.383 Calculates the CDF P(μ-x≤X≤μ+x).

The History Detail

Normal Distribution CDF 2 Tails
          0.500 : The x value.
           10.0 : The mean of the distribution.
           1.00 : The standard deviation of the distribution.
          0.383 : The normal CDF, 2 tail P(μ-x≤X≤μ+x).
Result:	 0.383

Example 2

What is the value of x for a cdf of 0.8?

These keystrokes assume the values from example 1.

Value Keystrokes Display Description
.8 P(μ±x) 0.800 Stores the cdf value.
  x 1.28 Calculates the x value.

The History Detail

Normal Distribution CDF 2 Tails
Solving for x, x value, with initial value (guess) of 0.500
           1.28 : The x value.
           10.0 : The mean of the distribution.
           1.00 : The standard deviation of the distribution.
          0.800 : The normal CDF, 2 tail P(μ-x≤X≤μ+x).
Result:	 1.28

Reference:

Normal distribution - Wikipedia