Decide which probability distribution binomial,geometric, or Poisson applies to

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Bankruptcies: The mean number of bankruptcies filed per minute in the United States in a recent year was about two. Find the probability that (a) exactly five businesses will file bankruptcy in any given minute, (b) at least five businesses will file bankruptcy in any given minute, and (c) more than five businesses will file bankruptcy in any given minute.

Mar 27th, 2015

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

Mar 27th, 2015

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