Poisson Dist.

Question

The mean number of business failure per hour in the U.S. is about 8 and is approximately Poisson distributed. Find the probability that tomorrow (a 24-hour period) will have more than 200 business failures.

Answer 1

You can safely bet that it will NOT happen.

 

The Poisson Distribution is exp(-lamba) * lambda^k / k!

lambda = 8, as given in the problem, is the average number of business failures every hour.

 

To achieve this goal, there must be at least 9 business failures every hour for the next day.

 

P(x=9) = exp(-8)*8^9/9! = 0.045645347

 

This number raised to the power 24 is approximately 6.7 * 10^-33