# 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.$\normal Normal\ distribution\ N(x,\mu,\sigma)\\[10](1)\qquad probability\ density\\\hspace{30}f(x,\mu,\sigma)={\large\frac{1}{\sqrt{2\pi}\sigma}e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}}\\(2)\qquad lower\ cumulative\ distribution\\\hspace{30}P(x,\mu,\sigma)={\large\int_{\small-\infty}^{\hspace{25}\small x}}f(t,\mu,\sigma)dt\\(3)\qquad upper\ cumulative\ distribution\\\hspace{30}Q(x,\mu,\sigma)={\large\int_{\small x}^{\hspace{25}\small\infty}}f(t,\mu,\sigma)dt\\$

Normal distribution
 [1-5] /5 Disp-Num5103050100200
[1]  2017/03/29 05:16   Male / 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!
[2]  2016/07/26 23:16   Female / 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?
[3]  2016/01/23 11:56   Male / 50 years old level / A teacher / A researcher / Very /
Purpose of use
Check against the values I calculated using a Runge Kutta 4th order numerical method. What numerical method was used to generate these values?
[4]  2011/05/24 08:10   Male / 40 years old level / Self-employed people / Very /
Purpose of use
interest
Comment/Request
This site is very good, well written - clear. A great example to others. Thank you for putting this resource on-line.
[5]  2009/12/02 04:52   - / - / A researcher / Very /
Purpose of use
Calculating probability points.
Comment/Request
Terrific site.

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