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Cars arrive to a gas station according to a Poisson distribution with a mean of 4...

Cars arrive to a gas station according to a Poisson distribution with a mean of 4 cars per hour. Use Excel or StatCrunch to solve.

a. What is the expected number of cars arriving in 2 hours, or λt?

b. What is the probability of 6 or less cars arriving in 2 hours? ROUND TO FOUR (4) DECIMAL PLACES.

c. What is the probability of 9 or more cars arriving in 2 hours? ROUND TO FOUR (4) DECIMAL PLACES.

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

(A) Expected number of cars arriving in 2 hours = (number of cars per hour)*(number of hours)

= 4*2

= 8 cars per 2 hours

(B) Probability of 6 or less can be found directly using POISSON function in excel

Using excel function POISSON(x,mean,cumulative)

setting x = 6, mean = 8 and cumulative =TRUE for 6 or less

this implies

= POISSON(6,8,TRUE)

= 0.3134

(C) Probability of 9 or more = 1 - Probability of at least 8

= 1 - POISSON(x,mean,cumulative)

setting x = 8, mean = 8 and cumulative =TRUE for 6 or less

this implies

= 1 - POISSON(8,8,TRUE)

= 1-0.5925

= 0.4075

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