SOLUTION: if a bank receives on the average 6 bad checks perday what are the proba bilities that it will receive 1) 4 bad checks on any given day. 2) 10 bad checks over any 2 consecutive

Question 1015833: if a bank receives on the average 6 bad checks perday what are the proba bilities that it will receive 1) 4 bad checks on any given day. 2) 10 bad checks over any 2 consecutive days.
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
If a bank receives on the average 6 bad checks perday what are the proba bilities that it will receive 1) 4 bad checks on any given day. 2) 10 bad checks over any 2 consecutive days.

Solution:
It is necessary to recognize the problem satisfies the conditions of the Poission distribution, namely:
a. The experiment results in outcomes that can be classified as successes or failures.
b. The average number of successes (μ) that occurs in a specified region is known.
c. The probability that a success will occur is proportional to the size of the region.
d. The probability that a success will occur in an extremely small region is virtually zero.

The probability is given by:
P(x; μ) = (e^(- μ))*(μ^x) / x!
where μ=mean, x=number of occurrences

Case 1: μ=6, x=4
P(6;4)=

Case 2: μ=12, x=10
P(10;12)=

ref:http://stattrek.com/probability-distributions/poisson.aspx
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