Final answer:
To find the probability that the schools in this town will close for 4 days during the coming season, we can use the Poisson distribution. The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space.
Step-by-step explanation:
To find the probability that the schools in this town will close for 4 days during the coming season, we can use the Poisson distribution. The Poisson distribution is used to model the number of events that occur in a fixed interval of time or space, given the average rate of occurrence.
In this case, the average number of days schools are closed due to a cholera outbreak is 4. We can use this average as the parameter for the Poisson distribution.
The probability mass function (PMF) of the Poisson distribution is given by the formula:
P(X=k) = (e^(-λ) * λ^k) / k!
where X is the number of events, λ is the average rate of occurrence, and k is the number of events we are interested in.
In this case, we are interested in the probability that the schools will close for 4 days, so k=4. Substituting λ=4, the formula becomes:
P(X=4) = (e^(-4) * 4^4) / 4!
Calculating the value of this expression will give us the probability that the schools will close for 4 days during the coming season.