Question

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.

Answer 1

I have answered the question below

Please up vote for the same and thanks!!!

Do reach out in the comments for any queries

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 N^x/x!

for 30 minutes (15*2) it will be e^-2 2 and (15 *1) e^-11^x 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