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In: Statistics and Probability

Patients arrive at the emergency room of Mercy Hospital at the average rate of 12 in...

Patients arrive at the emergency room of Mercy Hospital at the average rate of 12 in 60 minutes. what is the probability that 10 patients will arrive in 60 minutes? What is the probability that 4 patients will arrive in 30 minutes?

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Expert Solution

Let N(t) be the number of patients arriving at the emergency room of Mercy Hospital during a period of t minutes.  Patients arrive at the emergency room of Mercy Hospital at the average rate of 12 in 60 minutes or 12/60=0.2 per minute. We can say that N(t) has a Poisson distribution with rate .

The probability that N(t)=n patients will arrive in t minutes is

what is the probability that 10 patients will arrive in 60 minutes?

the probability that 10 patients will arrive in t=60 minutes is

ans: the probability that 10 patients will arrive in 60 minutes is 0.1048

What is the probability that 4 patients will arrive in 30 minutes?

the probability that 4 patients will arrive in t=30 minutes is

ans: the probability that 4 patients will arrive in 30 minutes is 0.1339

orchestra answered 2 years ago
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