Question

1. Assume that the number of bankruptcies for family owned businesses have a mean of three per month.

   1. What is the probability of no bankruptcies this month?

   2. What is the probability of more than 17 bankruptcies in the first quarter of 2020?

   3. If your friend told you that 5 family owned businesses bankrupted this month, would you believe him?

      Explain briefly using probabilities.

Answer 1

this is Poisson distribution with parameter λ=3

1)

probability of no bankruptcies this month =P(X=0) =e^-33⁰/0! =0.0498

2)

expected number of bankruptcies in the first quarter (3 months) =3*3 =9

probability of more than 17 bankruptcies in the first quarter of 2020:

P(X>18)=1-P(X<=17)=

1-∑x=017 e-9*9x/x!=

0.0053

if using ti-84 use command :1-poissoncdf(9,17)

if using excel use commannd :1-poisson(17,9,true)

3)

P(5  family owned businesses bankrupted this month) =P(X=5)=e^-33⁵/5! =0.1008

since probability of this or more extreme event is greater than 0.05 , therefore this is not an unusual event.

we can believe his information since this is not an unusual event.