Wutao from Homework 2 has finished his dissertation! He has flown in from Washin

Question

Wutao from Homework 2 has finished his dissertation! He has flown in from Washington and he is about to defend the dissertation he spent so much time writing. To celebrate, he declares a night of fun at the Neon Cactus. He calls up all his friends. It turns out it is a Thursday night so the Neon Cactus is packed! He assumes each person attending is independent of all the others. From a discussion with a bartender, Wutao learns on average a new person enters the Neon Cactus every 2 minutes.

a) Let N be the number of people who arrive between 9:00 and 10:00 PM. What are the distribution, parameter(s), and support of N?

b) What is the probability 25 people entered between 9:00 and 10:00 PM and 33 people between 10:30 and 11:30 PM?

c) What is the probability that 55 people enter between 9:00 PM and 11:00 PM?

d) What is the expected number of people that will arrive at the Neon Cactus between 9:00 and 11:00 PM?

e) What is the standard deviation of the number of people who arrive at the Neon Cactus between 9:00 and 10:00 PM?

Explanation / Answer

Ans:

a)Poisson distribution with mean=1 person/2 min

b)mean=1 person/2 min=30 person/60 min or 1 hr

P(k=25)=POISSON(25,30,FALSE)=0.0511

P(k=33)=POISSON(33,30,FALSE)=0.0599

c)mean=1 person/2 min=60 persons/120 min or 2 hrs

P(x=55)=POISSON(55,60,FALSE)=0.0433

d)mean=1 person/2 min=60 persons/120 min or 2 hr

e)standard deviation=sqrt(30)=5.48

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