Normal Distribution

For a   N(μ,σ²) distributed random variable X with given expected value μ and variance  σ², You may calculate

 

- density function    

- and distribution function

The diagram of the density function f(x) is often called Gaussian curve, or bell shaped curve. The distribution function  Φ(x) is designated as Gaussian error function, because, according to Gauss, this distribution is assumed for the random errors in astronomical observations.

Expected value  μ  and variance  σ² are entered. For  μ=0  and  σ=1  you receive the standardized normal distribution.

Example:

  μ = 5 ,      σ = .75

         x                     ƒ(x)                   Φ(x)      
  —————       –—————     —————–
  2                       0,00017844      0,00003167   
  2,33333333      0,00095649      0,00018859
  2,66666666      0,00420802      0,00093192
  2,99999999      0,01519465      0,00383038
  3,33333332      0,04503153      0,01313415
  3,66666665      0,10953585      0,03772017
  3,99999998      0,21868009      0,09121120
  4,33333331      0,35832381      0,18703139
  4,66666664      0,48189843      0,32836063
  4,99999997      0,53192304      0,49999998
  5,3333333        0,48189845      0,67163934
  5,66666663      0,35832383      0,81296859
  5,99999996      0,21868012      0,90878878
  6,33333329      0,10953586      0,96227982

See also:

Setting the graphics
Wikipedia: Normal distribution