Compute Probabilities of a Poisson Random Variable
-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 9 tickets per day. Find the probability that less than six tickets are written on a randomly selected day from this distribution.
A) 0.115691
B) 0.206781
C) 0.884309
D) 0.793219

Question

Quizplus · Accepted Answer

The probability that less than six tickets are written on a randomly selected day from this distribution is 0.115691. This can be calculated using the Poisson distribution formula:P(X = k) = (e^-λ * λ^k) / k!where:λ is the mean of the distributionk is the number of tickets writtenIn this case, λ = 9 and k = 6. Plugging these values into the formula, we get:P(X < 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)= (e^-9 * 9^0) / 0! + (e^-9 * 9^1) / 1! + (e^-9 * 9^2) / 2! + (e^-9 * 9^3) / 3! + (e^-9 * 9^4) / 4! + (e^-9 * 9^5) / 5!= 0.000045 + 0.000405 + 0.001826 + 0.006389 + 0.018167 + 0.040876= 0.115691