What is the range of expected errors in a day within +/- 2 standard deviations if there are 2,000,000 such transactions each day?

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?
A . 80 to 120 errors in a day
B . 60 to 80 errors in a day
C . 0 to 200 errors in a day
D . 90 to 110 errors in a day

Answer: A

Explanation:

Error rates are generally modeled using thePoisson distribution. Recall that the Poisson distribution has only one parameter – – 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.