John Thurgood founded a company that translates Chinese books into English. His company is currently testing a computer-based translation service. Since Chinese symbols are difficult to translate, John assumes the computer program will make some errors, but then so do human translators. The computer error rate is supposed to be an average of 3 per 400 words of translation. Suppose John randomly selects a 1,200-word passage. Assuming that the Poisson distribution applies, if the computer error rate is actually 3 errors per 400 words, determine the probability that no errors will be found.
A) 0.0001
B) 0.0141
C) 0.0415
D) 0.4557

Question

Quizplus · Accepted Answer

The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space. In this case, the interval is the 1,200-word passage, and the event is a computer error. The average number of errors per 400 words is 3, so the average number of errors per 1,200 words is 9. The probability of no errors is given by the Poisson distribution with λ = 9:P(X = 0) = e^(-9) * 9^0 / 0! = 0.0001

John Thurgood Founded a Company That Translates Chinese Books into English