SOLUTION: An insurance company has an average of 9 claims per week. What is the probability that during the next week exactly 7 will be filed.

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Question 194883: An insurance company has an average of 9 claims per week. What is the probability that during the next week exactly 7 will be filed.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
An insurance company has an average of 9 claims per week. What is the probability that during the next week exactly 7 will be filed.

If X is the number of successes in an interval
of fixed length and X follows a Poisson process 
with mean mu, then the probability that 
X = x is
         
P%28X=x%29+=+%28%28mu%5Ex%29%2Fx%21%29e%5E%28-mu%29
         
In your problem, mu=9, x=7, so

P%28X=7%29+=+%28%289%5E7%29%2F7%21%29e%5E%28-9%29=.1171161245 

Edwin