A fire and emergency rescue service receives calls for assistance at a rate of ten per day. Teams man the service in twelve hour shifts. Assume that requests for help form a Poisson process

(i) What is the probability that a team would receive six requests for help in a shift?

(ii) What is the probability that a team has no requests for assistance in a shift?

To solve these questions, we use the Poisson distribution, which is applicable for a Poisson process. The Poisson distribution gives the probability of a given number of events occurring in a fixed interval of time, given a known average rate of occurrence.

Given:

• The rate of requests per day = 10 calls per day.

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