A regional director responsible for business development in the state of pennsylvania is concerned about the number of small business failures. if the mean number of small business failures per month is 10, what is the probability that exactly four small businesses will fail during a given month? assume that the probability of a failure is the same for any two months and that the occurrence or nonoccurrence of a failure in any month is independent of failures in any other month.

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Zachariah

Mathematics

12 March, 22:05

A regional director responsible for business development in the state of pennsylvania is concerned about the number of small business failures. if the mean number of small business failures per month is 10, what is the probability that exactly four small businesses will fail during a given month? assume that the probability of a failure is the same for any two months and that the occurrence or nonoccurrence of a failure in any month is independent of failures in any other month.

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Philip Sanford · Answer 1

The question is a poisson distribution problem with mean = 10 and x = 4.

P (x, mean) = (e^-mean) (mean^x) / x! = (e^-10) (10^4) / 4! = 0.4540 / 24 = 0.0189

Therefore, the probability that exactly four small businesses will fail in a given month is 0.0189 or 1.89%.