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

Answer:

B) 0.1487

Step-by-step 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:

$P(X=k)=\frac{\lambda^{k} *e^{-\lambda} }{k!}$

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:

$P(X=5)=\frac{6.4^{5} *e^{-6.4} }{5!} =\frac{17.84083537}{120} =0.1486736281\approx0.1487$