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 three tickets are written on a randomly selected day.

0.0204 = 2.04% probability that fewer than three tickets are written on a randomly selected day.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval.

Poisson distribution with a mean of 7.5.

This means that .

Find the probability that fewer than three tickets are written on a randomly selected day.

This is:

So

0.0204 = 2.04% probability that fewer than three tickets are written on a randomly selected day.