Question

Problem: The mean number of bankruptcies filed per minute in the ` States in a recent year was about two. Find the probability that exactly five businesses will file bankruptcy in any given minute.

Answer 1

The number of companies is quite large. That is, n is quite large.
The probability that a company declares bankruptcy is quite small , p is quite small.
np = the mean number of bankruptcies = 2  = a finite number.
Hence we can apply Poisson distribution for the data.
P (x=5 | mean =2) = e-2 25/5! = e-2 * 32/120 = 0.036089
Alternatively 
=poisson(5,2,0) = 0.036089
P(x≥ 5 | mean =2) = 1- P( x ≤ 4) = 1- e-2 (1+2+22/2!+23/3!+24/4!)= 1-e-2 (1+2+2+8/6+16/24)= 1-e-2(7)
  =0.052653
Alternatively
= 1- poisson(4,2,1) =0.052653
P(X > 5 | mean =2) = 1- p(x
 ≤ 5) =1- e-2 (1+2+22/2!+23/3!+24/4!+25/5!)= 1-e-2(7+4/15)
  =0.016564
alternatively=1-poisson(5,2,1)
=0.016564