Question

Statistics from the Riverside Police Department show that in the last 12 years there were 648 reported crimes in the city. Find the probability that there is exactly 1 reported crime on any given day. Assume that there are 365 days in each year (i.e. ignore leap years) to simplify your calculations.

Answer 1

Answer:

12.76% probability that there is exactly 1 reported crime on any given 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:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

Statistics from the Riverside Police Department show that in the last 12 years there were 648 reported crimes in the city.

Each year has 365 days. We want the mean for a day. So

$\mu = \frac{648}{12*365} = 0.1479$

Find the probability that there is exactly 1 reported crime on any given day.

This is P(X = 1).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = 1) = \frac{e^{-0.1479}*(0.1479)^{1}}{(1)!} = 0.1276$

12.76% probability that there is exactly 1 reported crime on any given day.