Returns the probability of X <= z for a normal distribution.
PROBN(z, mean, std)
z |
- |
A real or series. The z value. |
mean |
- |
Optional. A real, the mean of the distribution. Defaults to 0.0. |
std |
- |
Optional. A real, the standard deviation of the distribution, where |
A real or series, the probability that a value is less than or equal to the input z value for a normal distribution with the given mean and standard deviation.
For the input value z, returns the probability p where P(X <= z) = p.
probn(0)
returns 0.5, the probability that a value is less than or equal to 0.0 for a normal distribution with a mean of 0.0 and a standard deviation of 1.0.
In probabilistic terms, given the normal distribution N(0, 1), i.e. mean of 0, variance of 1:
P(X <= 0.0) = 0.5
probn(2, 1, 2) - probn(0, 1, 2)
returns 0.382925, the probability that a value is less than or equal to 2 and greater than or equal to 0.0 for a normal distribution with a mean of 1.0 and a standard deviation of 2.0
In probabilistic terms, given the normal distribution N(1, 4), i.e. mean of 1, variance of 4:
P(0.0 <= X <= 2.0) = 0.382925
1 – probn(.5)
returns 0.30853754, the probability that a value is greater than 0.5 for a normal distribution with a mean of 0.0 and a standard deviation of 1.0
probn(invprobn(.3))
returns 0.3, indicating that PROBN and INVPROBN are inverse functions.
probn(-3..0.01..3)
displays the normal cumulative distribution function from –3 to 3.
The result is NaN where std
The probability density function, f(x), for normally distributed random values is:
where μ is the mean, σ is the standard deviation and σ^{2} is the variance. The cumulative distribution function,
where erf(x) is the error function implemented by ERF. PROBN uses ERF to evaluate the area under the normal distribution curve. Note that
Approximately 68% of the values from a normal distribution are within one standard deviation away from the mean. Approximately 95% of the values lie within two standard deviations and approximately 99.7% are within three standard deviations. This is known as the 3-sigma rule.
See INVPROBN to calculate the inverse normal cumulative distribution function. PROBN and INVPROBN are inverse functions.
See PDFNORM to generate the normal density function.
See GNORMAL to generate a series of normally distributed random values.