in Advanced Math New Covid-19 patients arrive at the emergency room in Sultan Qaboos Hospital at a mean arrival rate of 18.8 patients per hour. Use Poisson distribution to compute the probability that at least three new patients will arrive at the emergency room within a 15-minute interval?

amanf 2020-11-30 Answered
in Advanced Math
New Covid-19 patients arrive at the emergency room in Sultan Qaboos Hospital at a mean arrival rate of 18.8 patients per hour. Use Poisson distribution to compute the probability that at least three new patients will arrive at the emergency room within a 15-minute interval?
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Expert Answer

liannemdh
Answered 2020-12-01 Author has 106 answers

Step 1
Given that,
New Covid-19 patients arrive at the emergency room in Sultan Qaboos Hospital at a mean arrival rate of 18.8 patients per hour.
Mean arrival rate in 15 minute can be calculated as follows:
λ=19.960×15
=4.7
Step 2
The probability that at least three new patients will arrive at the emergency room within a 15-minute interval can be calculated as follows:
P(X3)=1P(X<3)
=1[P(X=0)+P(X=1)+P(X=2)]
=1[e4.74.700!+e4.74.711!+e4.74.722!]
=1e4.7[1+4.7+11.045]
=1-0.1523
=0.8477
Thus, the probability that at least three new patients will arrive at the emergency room within a 15-minute interval is 0.8477.

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