The Number X of People Entering the Intensive Care Unit

question 21

Essay

The number x of people entering the intensive care unit at a particular hospital on any one day has a Poisson probability distribution with mean equal to four persons per day.
What is the probability that the number of people entering the intensive care unit on a particular day is two?
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What is the probability that the number of people entering the intensive care unit on a particular day is Less than or equal to two?
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Is it likely that x will exceed ten?
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Explain.
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Definitions:

Incidental Beneficiaries

Individuals or entities that unexpectedly benefit from a contract, despite not being directly involved in its formulations.

Creditor Beneficiary

A third party that benefits from a contract made between two other parties, especially regarding debt repayment.

Donee Beneficiary

In contract law, a person who benefits from the execution of a contract, though not one of the principle parties involved.

Incidental Beneficiary

A third party who benefits from a contract indirectly or unintentionally, without being a direct party to the agreement.