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

B) 0.1487

Step-by-step explanation:

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

Where:

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

.25

step-by-step explanation:

9 x 8 divided by (5-3)=36