9.A service station has one gasoline pump. Cars wanting gasoline arrive according to a Poisson process at a meanrate of 15 per hour. However, if the pump already is being used, these potential customers may balk (drive onto another service station). In particular, if there are n cars already at the service station, the probability that annarriving potential customer will balk is for n = 1, 2, 3. The time required to service a car has an exponential3distribution with a mean of 4 minutes.(a) Construct the rate diagram for this queueing system.(b) Find the steady-state probability distribution of the number of cars at the station.(c) Find the expected waiting time (including service) for those cars that stay.

Answered: Image /qna-images/answer/f1d7876a-7f40-43a0-900e-7685e8c17f12.jpg

Answered: (a) Construct the rate diagram for this…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Don't hand writing
For 10 percent of the products in a category, a firm fails to satisfy all demand during themonth. What is its in-stock probability?
Mara Jade is analyzing the fire damage losses in her insurance firm that occurred over a one-year period, based on the following data: Number of Claims Filed Number of Houses Total Number of Claims 0 9,555 0 1 160 160 2 20 40 Fill in the table and calculate the average frequency of loss. Use the information in the table to estimate a probability distribution for the frequency distribution of losses.
12. Calculate the expected life of refrigerators at the age of 7 using the following data. Age: up 2 2-4 4-6 6–8 8-10 10-12 16 13 7 5 4 Girls:
The graph of the discrete probability to the right represents the number of live births by a mother 42 to 46 years old who had a live birth in 2015. Complete parts (a) through (d) below. (...) A 0.30- 0.25- 0.20- 0.15- 0.10- 0.05- 0.00- 0.232 1 0.270 2 0.472 0.114 0.098 0.021 0.039 0.054 ? 3 4 5 Number of Live Births 6 8 (a) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her fourth live birth in that year? (Type an integer or a decimal.) (b) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her fourth or fifth live birth in that year? (Type an integer or a decimal.) (c) What is the probability that a randomly selected 42- to 46-year-old mother who had a live birth in 2015 has had her sixth or more live birth in that year? (Type an integer or a decimal.) (d) If a 42- to 46-year-old mother who had a live birth in 2015 is randomly selected, how many live births…
Q3
Suppose a life insurance company sells a $230,000 one-year term life insurance policy to a 20-year-old female for $370.The probability that the female survives the year is 0.999464. Compute and interpret the expected value of this policy to the insurance company.
A barbershop is operated by one barber and has a space capacity to accommodate for a total of 6 customers (including the one in service). If a customer comes to this shop and finds it full, he goes to other shops. Customers arrive according to Poisson distribution at a rate of 4.1 customers per hour. The barber’s service time is exponential and he can serve at a rate of 7.1 customers per hour. a. What is the probability that the barber is free? Answer = Answer b. What is the expected number of people in the system? Answer = Answer c. What is the expected waiting time in the queue? Answer = Answerhours. (hint: use effective arrival rate)
The less correlated the securities in a portfolio, Select one: O a the higher the diversifiable risk. O b. the higher the portfolio risk. O c. the lower the portfolio risk. Od the lower the unsystematic risk.
Suppose a life insurance company sells a $230,000 one-year term life insurance policy to a 20-year-old female for$240. The probability that the female survives the year is 0.999463. Compute and interpret the expected value of this policy to the insurance company.
Suppose a life insurance company sells a $280,000 one-year term life insurance policy to a 24-year-old female for $180. The probability that the female survives the year is 0.999522. Compute and interpret the expected value of this policy to the insurance company.
Each day, John's mother gives him money before he goes to school: 50% of the time he gets $5, 35% of the time he gets $10 and the rest of the time he gets $20. Determine the expectation and variance for how much money John gets each day. For the next 100 school days, John plans to save all the money his mother gives him. What is the approximate probability he is able to save more than $1000? Assume independence. If he realizes he has to spend an average of $4 a day with a standard deviation of $0.75, what is the approximate probability that he saves less than $400? Assume independence.

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

(a) Construct the rate diagram for this queueing system. (b) Find the steady-state probability distribution of the number of cars at the station. (c) Find the expected waiting time (including service) for those cars that stay.