Question

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   
0 0
Add a commentTranscribed image text
Next >

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

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In a gas station there is one gas pump. Cars arrive at the gas station according...
In a gas station there is one gas pump. Cars arrive at the gas station according to a Poisson proces. The arrival rate is 20 cars per hour. An arriving car finding n cars at the station immediately leaves with probability qn = n/4, and joins the queue with probability 1−qn, n = 0,1,2,3,4. Cars are served in order of arrival. The service time (i.e. the time needed for pumping and paying) is exponential. The mean service time is 3...
The number of cars arriving at a gas station can be modelled by Poisson distribution with...
The number of cars arriving at a gas station can be modelled by Poisson distribution with the average rate of 5 cars per 10 minutes. a. The probability that one car will arrive to a gas station in a 5 -minute interval is _________ b. The probability that at least one car will arrive to the gas station in a 10 - minute interval is ______
Cars arrive at a toll booth according to a Poisson process with mean 60 cars per...
Cars arrive at a toll booth according to a Poisson process with mean 60 cars per hour. If the attendant makes a three minute phone call, what is the probability that the number of cars passing through the toll booth during the call is between 2 and 4, inclusive?
The cars arriving at a gas station is Poisson distributed with a mean of 10 per...
The cars arriving at a gas station is Poisson distributed with a mean of 10 per minute. Determine the number of pumps to be installed if the firm wants to have 50% of arriving cars as zero entries (cars serviced without waiting).
The number of cars arriving at a petrol station in a period of t minutes may...
The number of cars arriving at a petrol station in a period of t minutes may be assumed to have a Poisson distribution with mean 720t. Use this information to answer questions 31-32. Find the probability that exactly 12 cars will arrive in one and half hours. Find the probability that more than 24 cars will arrive in an hour.
Customers arrive to a savings bank according to a Poisson distribution with mean 3 per hour....
Customers arrive to a savings bank according to a Poisson distribution with mean 3 per hour. Then, they either complete a transaction with a bank teller or meet with a financial officer, and leave the bank when they are done. What is the probability that exactly 2 customers arrive in the next three hours? What is the probability that at least 3 customers arrive in the next two hours? What is the probability that nobody arrives in the next 30...
The number of cars that arrive at a certain intersection follows the Poisson distribution with a...
The number of cars that arrive at a certain intersection follows the Poisson distribution with a rate of 1.9 cars/min. What is the probability that at least two cars arrive in a 2 minutes period?
Suppose that buses are coming into a station at an average rate 4 per hour according...
Suppose that buses are coming into a station at an average rate 4 per hour according to a Poisson process. We start to account the buses from 1:00 (pm). (a) What is the probability that no buses arrive between 1:00pm-2:00pm? (b) What is the probability that three buses arrive between 1:00pm-3:00pm? (c) What is the probability that the third bus takes more that 3 hours to arrive? (d) What is the expected time the third bus arrive to the station?
At a train station, international trains arrive at a rate λ = 1 (poisson distribution). At...
At a train station, international trains arrive at a rate λ = 1 (poisson distribution). At the same train station national trains arrive at rate λ = 2 (poisson distribution). The two trains are independent. What is the probability that the first international train arrives within 3 times the arrival time of the first national train?
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α...
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α = 8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t. (Round your answers to three decimal places.) (a) What is the probability that exactly 7 small aircraft arrive during a 1-hour period?____________ What is the probability that at least 7 small aircraft arrive during a 1-hour period?_____________ What...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT