Answer:
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:
![P(X=k)=\frac{\lambda^{k} *e^{-\lambda} }{k!}](https://tex.z-dn.net/?f=P%28X%3Dk%29%3D%5Cfrac%7B%5Clambda%5E%7Bk%7D%20%2Ae%5E%7B-%5Clambda%7D%20%7D%7Bk%21%7D)
Where:
![\lambda=Mean\\k=number\hspace{3}of\hspace{3}events\\e=Euler's\hspace{3}number](https://tex.z-dn.net/?f=%5Clambda%3DMean%5C%5Ck%3Dnumber%5Chspace%7B3%7Dof%5Chspace%7B3%7Devents%5C%5Ce%3DEuler%27s%5Chspace%7B3%7Dnumber)
So, the probability that exactly 5 bankruptcies occur next month is:
![P(X=5)=\frac{6.4^{5} *e^{-6.4} }{5!} =\frac{17.84083537}{120} =0.1486736281\approx0.1487](https://tex.z-dn.net/?f=P%28X%3D5%29%3D%5Cfrac%7B6.4%5E%7B5%7D%20%2Ae%5E%7B-6.4%7D%20%7D%7B5%21%7D%20%3D%5Cfrac%7B17.84083537%7D%7B120%7D%20%3D0.1486736281%5Capprox0.1487)
It's greater than 117.859. Hope this helps