Question

# ANSWER THE FOUR PARTS OR DON'T ANSWER AT ALL. Mixed Poisson/exponential Customers arrive at the drive-up...

1. Mixed Poisson/exponential

Customers arrive at the drive-up window of a fast-food restaurant at a rate of 2 per minute during the lunch hour (12-1pm).

a. What is the probability that exactly 3 customers will arrive in 1 minute? 1 customer will arrive in 5 minutes?

b. What is the probability that no customers will arrive in 2 minutes?

c. Given a customer has just arrived, what is the probability that the next customer will arrive within 1 minute? 2 minutes?

d. Given a customer has just arrived, what is the probability the next customer will NOT arrive within the next 2 minutes?

a)P( exactly 3 customers will arrive in 1 minute )=e-2*23/3! =0.180447

P( 1 customer will arrive in 5 minutes )=e-2*5*(5*2)1/1! =0.000454

b) probability that no customers will arrive in 2 minutes =P(X=0)=e-2*2*(2*2)0/0! =0.018316

c)

probability that the next customer will arrive within 1 minute =1-P(X=0)=1-e-2*20/0! =0.864665

probability that the next customer will arrive within 2 minute =1-P(X=0)=1-e-2*2*(2*2)0/0! =0.981684

d)

probability the next customer will NOT arrive within the next 2 minutes = e-2*2*(2*2)0/0! =0.018316