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.

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