Hello, I have this problem from my Statistic class and I don't understand it. Can you write step by step to solve this.
A hospital keeps track of its emergency room traffic. The records indicate that beginning at 6:00 pm on any given day there will be 4 patients arriving per hour. Determine the probability that the third patient arrives between 6:15 pm and 6:30 pm.
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Answer:
We have to find that the probability of third patient arriving between 6:15 pm and 6:30 pm
This can be calculated as =Probability of (3 or more preople arrive in 30 minutes)-Probability of (3 or more people arriving in 15 minutes)
exponentrial distribution expected interarrival time
=60/4 =15 minutes
The cdf function will be 1 - e-(N)*X Nx/x!
for 30 minutes (15*2) it will be e-2 2 and (15 *1) e-11x for 15 minutes
=(1-
)-(1-
)
= (1 - (e-220/0! + e-221/1! + e-222/2!) ) + (1 - (e-110/0! + e-111/1! + e-112/2! ))
= (1- 0.135335 - 0.2707 - 0.2707) + ( 1 - 0.3679 - 0.36789 - 0.184)
=0.323324- 0.08030 =0.243022
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