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briancastrodiaz10

25.01.2023

Mathematics

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:

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

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:

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

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