Question

A life insurance company has determined that each week (7 days) an average of seven claims is filed in its Nashville branch. Define x as the number of claims filed in a one-week period. What is the probability that during the next 3 days, two claims will be filed?

Answer 1

Answer:

The probability of having two claims in three days is 0.225.

Step-by-step explanation:

This type of process can be modeled by the Poisson distribution.

This distribution has a rate, that in this case is x: number of claims filled in a one-week period.

The probabilty density function can be written as

$P(y=k)=\frac{(xt)^ke^{-xt}} {k!}$

In this case, $t =3 \,days =3/7\,weeks= 0.429\,weeks$.

The probablity of having two claims in three days is:

$P(y=2)=\frac{(7*(3/7))^2e^{-7*(3/7)}} {2!}=\frac{3^2*e^{-3}}{2}=\frac{9*0.05}{2}=0.225$

The probability of having two claims in three days is 0.225.