Question

The Department of Commerce in a particular state has determined that the number of small businesses that declare bankruptcy per month is approximately a Poisson distribution with a mean of 6.4. Find the probability that exactly 5 bankruptcies occur next month.

A) 0.0589
B) 0.1487
C) 0.1987
D) 0.2987

Answer 1

B) 0.1487

Explanation:

Let
`X` be the discrete random variable that represents the number of events observed over a given time period. If
`X` follows a Poisson distribution, then the probability of observing
`k` events over the time period is:

`P(X=k)=(\lambda^(k) *e^(-\lambda) )/(k!)`

Where:

`\lambda=Mean\\k=number\hspace{3}of\hspace{3}events\\e=Euler's\hspace{3}number`

So, the probability that exactly 5 bankruptcies occur next month is:

`P(X=5)=(6.4^(5) *e^(-6.4) )/(5!) =(17.84083537)/(120) =0.1486736281\approx0.1487`