A bank expects the error rate in transaction data entry for a particular business process to be 0.005%. What is the range of expected errors in a day within +/- 2 standard deviations if there are 2,000,000 such transactions each day?
Error rates are generally modeled using the Poisson distribution. Recall that the Poisson distribution has only one parameter - λ - which is its mean and also its variance.
In the given case, the mean number of errors is 2,000,000 x 0.005% = 100. Since this is the variance as well, the standard deviation is √100 = 10. Therefore the range of outcomes within 2 standard deviations of the mean is 100 +/- (2*10) = 80 to 120 errors in a day.
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