Answer:
B) 0.1487
Step-by-step explanation:
Let [tex]X[/tex] be the discrete random variable that represents the number of events observed over a given time period. If [tex]X[/tex] follows a Poisson distribution, then the probability of observing [tex]k[/tex] events over the time period is:
[tex]P(X=k)=\frac{\lambda^{k} *e^{-\lambda} }{k!}[/tex]
Where:
[tex]\lambda=Mean\\k=number\hspace{3}of\hspace{3}events\\e=Euler's\hspace{3}number[/tex]
So, the probability that exactly 5 bankruptcies occur next month is:
[tex]P(X=5)=\frac{6.4^{5} *e^{-6.4} }{5!} =\frac{17.84083537}{120} =0.1486736281\approx0.1487[/tex]
