The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 8.9. Find the probability that exactly four tickets are written on a randomly selected day.
A) .035656
B) .941567
C) .058433
D) .964344

Question

Quizplus · Accepted Answer

The probability of observing exactly k events in a Poisson distribution is given by the formula: P(X=k) = (λ^k * e^(-λ)) / k!, where λ is the average rate (mean) of occurrence. Here, λ = 8.9 and k = 4. Plugging these values into the formula gives the probability of exactly four tickets being written.

The University Police Department Must Write, on Average, Five Tickets