`' VBA's intrinsic Rnd function returns numbers evenly' distributed between 0 and 1. Each number in that' interval has equal probability of being returned' for any given function call.' This function NormRand returns a random number between' -infinity and +infinity distibuted normally around' zero and with standard deviation equal to 1 (i.e.' about 95% of the values are within the range -2 to +2,' this is a standard statistical result, often referred' to as a confidence interval).'' Common uses for such randomly distributed numbers occur' in finance, statistics and many real-world applications.' For example, if I wanted to simulate the heights of' children in a class I might postulate that their heights' would have mean=x and standard deviation=s. I might decide' at a value for s by suggesting that 95% of them should' have heights between x-2s and x+2s. It follows that we can' simulate the height of any one member of the (imaginary)' class of children = (s*NormRand + x).'' IMPORTANT: call Randomize before using NormRandFunction NormRand() As Double ' NormRand returns a randomly distributed drawing from a ' standard normal distribution i.e. one with: ' Average = 0 and Standard Deviation = 1.0 Dim fac As Double, rsq As Double, v1 As Double, v2 As Double Static flag As Boolean, gset As Double ' Each pass through the calculation of the routine produces ' two normally-distributed deviates, so we only need to do ' the calculations every other call. So we set the flag ' variable (to true) if gset contains a spare NormRand value. If flag Then NormRand = gset ' Force calculation next time. flag = False Else ' Don't have anything saved so need to find a pair of values ' First generate a co-ordinate pair within the unit circle: Do v1 = 2 * Rnd - 1# v2 = 2 * Rnd - 1# rsq = v1 * v1 + v2 * v2 Loop Until rsq <= 1# ' Do the Math: fac = Sqr(-2# * Log(rsq) / rsq) ' Return one of the values and save the other (gset) for next time: NormRand = v2 * fac gset = v1 * fac flag = True End If End Function`

#### 7 Ways Technology Has Changed Traditional Payments

In today’s digital world, technology has changed how we make payments. From contactless cards to mobile wallets, it’s now easier