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
