Normal Distribution CDF Upper Tail Calculator

This CDF calculator computes the cumulative probability P(X>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 of P(X>x) as a function of any of the paramaters.

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

Example 1

Determine the probability of the new project achieving an ROI greater than 8% to assess if it aligns with the company's risk threshold. With an average expected ROI of 12% and a variability of 3%, calculate the upper tail probability P(X>8%) to ensure the investment's risk is within acceptable limits.

Value	Keystrokes	Display	Description
8	x	8.00	Stores the x value.
12	μ	12.0	Stores the μ (mean) value.
3	σ	3.00	Stores the σ (standard deviation) value.
	P(X>x)	0.909	Calculates the upper tail P(X>x).

The History Detail

Normal Distribution CDF Upper Tail
           8.00 : The x value.
           12.0 : The mean of the distribution.
           3.00 : The standard deviation of the distribution.
          0.909 : The normal cumulative distribution function, upper tail P(X>x).
Result:	 0.909

Example 2, Inverse

In Example 1, what is the value of x given a P(X>x) = 0.9?

These keystrokes assume the values from example 1.

Value	Keystrokes	Display	Description
.9	P(X>x)	0.900	Stores the P(X>x) value.
	x	8.16	Solves for the x value.

The History Detail

Normal Distribution CDF Upper Tail
Solving for x, x value, with initial value (guess) of 8.00
           8.16 : The x value.
           12.0 : The mean of the distribution.
           3.00 : The standard deviation of the distribution.
          0.900 : The normal cumulative distribution function, upper tail P(X>x).
Result:	 8.16

This Function Calculator will also solve for the values of the mean and standard deviation.

Reference:

Normal distribution - Wikipedia