# Normal distribution Calculator

## Calculates the probability density function and lower and upper cumulative distribution functions of the normal distribution.

 percentile x mean μ standard deviation σ σ＞0 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
The default value μ and σ shows the standard normal distribution.

Normal distribution
 [1-10] /13 Disp-Num5103050100200
[1]  2021/06/19 17:14   60 years old level or over / A teacher / A researcher / Useful /
Purpose of use
Estimating theoretical probability of an event at least 103 standard deviations below the mean (corresponds to some US monthly employment data during the 2020 Covid pandemic.)
[2]  2021/06/03 00:03   30 years old level / High-school/ University/ Grad student / Not at All /
Purpose of use
To check range that can be given by the user
Comment/Request
Cannot give range that can be given by the user to check the probability
from Keisan
To calculate for a specific range, please use Normal distribution (interval) Calculator.
[3]  2020/08/13 13:42   Under 20 years old / High-school/ University/ Grad student / Very /
Purpose of use
Calculating Gypsy IQ
[4]  2020/06/13 16:18   60 years old level or over / A teacher / A researcher / Very /
Purpose of use
Detection of the outliers. Comparison between confidence intervals based on the normal distribution and Tukey's fences for k = 1.5, 2.0, 2.5, 3.0
[5]  2019/07/09 00:32   40 years old level / An engineer / Very /
Purpose of use
IQ population measurements
[6]  2019/06/17 13:42   Under 20 years old / High-school/ University/ Grad student / Useful /
Purpose of use
Studying for a Bayesian statistics exam, and having a look at the distributions and playing around with the parameters, to get a better intuition.
Comment/Request
Would be nice if we could customise the grid steps (Delta x and y).
[7]  2019/05/15 09:49   50 years old level / An engineer / Very /
Purpose of use
Calculating probability of components being outside drawing tolerance when different CpK levels have been set.
[8]  2019/03/29 03:21   20 years old level / High-school/ University/ Grad student / Very /
Purpose of use
Reference
[9]  2017/03/28 20:16   60 years old level or over / A retired people / Very /
Purpose of use
Checking some double-double precision (about 32 decimals) fast code for bugs, sometimes in extreme areas for ratio of cdf to pdf (Mills Ratio). Very impressed to find that you do up to 50 decimals AND report extreme range where exponent can be essentially -infinity, apparently, most do not do that, so I could ask my extreme questions about the ratio, was expecting to have to do my own verification some other way. Thanks!
[10]  2016/07/26 14:16   Under 20 years old / Elementary school/ Junior high-school student / Useful /
Comment/Request
In a test in math, a class of 50 students obtained scores which are normally distributed with mean of 30 and whose SD is 5. How many students obtained scores lower that 25?

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