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 7.5. Find the probability that fewer than six tickets

Step-by-step explanation:

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 7.5. Find the probability that fewer than six tickets

Poisson Distribution

P = λ^k × e^-λ/k!

λ is the average of events

e is the euler's number

k is the number of events you want to know the probability

P(<6) = λ^k × e^-λ/k!

= 7.5^5 × e^-7.5/5! + 7.5^4 × e^-7.5/4! + 7.5^3 × e^-7.5/3! + 7.5^2 × e^-7.5/2! + 7.5^1 × e^-7.5/1!+ 7.5^0 × e^-7.5/0!

= 0.1093745947 + 0.0729163965 + 0.0388887448 + 0.0155554979 +0.0041481328 + 0.0005530844

a negative exponent is translated as follows:

so, we have