Binomial distribution va. Poisson distribution

Consider a bank which has a set of 550 loans. The bank estimates, that 4 out of

100 loans will get problems each year. Calculate the probability that 10,17,25 and

40 loans will get problems next year (use the binomial distribution and the poisson

distribution and compare the results).

I tried to use the binomial formula:

http://upload.wikimedia.org/math/a/c...5bf0bc3556.png

where n=550

k=10

p=0.04

My result is 0.18% which in my opinion makes not much sense as for 550 Loans there should be 22 defaults...

for the Poisson distribution I got 2.77^(-21)

I put in the figures in the following formula:

http://upload.wikimedia.org/math/9/d...62a481a198.png

where k=10

and lambda=0.04

Thx in advance

Re: Binomial distribution va. Poisson distribution

Binomial:

P[x={10,17,25,40}|550, .04] = {0.0017997, 0.051547, 0.066349, 0.00012953}

Poisson:

P[x={10,17,25,40}|550*0.04] = {{0.0020417, 0.051956, 0.06538, 0.00017013}

Re: Binomial distribution va. Poisson distribution

There are a few different order statistics formulas that include one for a maximum, one for a minimum and one for a distribution that is so many places from the minimum or the maximum.

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