3. A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back ofthe parking lot and then drive to the service window to pay for and receive their orders. Consider a two- channel operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 2 minutes for each channel.

3. A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back ofthe parking lot and then drive to the service window to pay for and receive their orders. Consider a two- channel operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 2 minutes for each channel.

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Description: 3. A fast-food franchise is considering operating a drive-up windowfood-service operation. Assume that customer arrivals follow a Poissonprobability distribution, with an arrival rate of 24 cars per hour, and that servicetimes follow an exponential

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...

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C). A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic arrivals follow a Poisson distribution with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes. (a) What is the probability that the clinic is empty (except for the dentist and staff)? (b) What is the probability that there are one or more patients in the system? (c) What is the probability that there are four patients in the system? (d) What is the probability that there are four or more patients in the system?
The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. 0.4 2300 T 0.3 2800 0.2 2500 2400 From/To A B C D A 0.2 0 0.3 0.3 B 0.3 0.2 0.5 0.4 C 0.1 0.5 0 0.3 D 0 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. c) What is the mean return time of Brand A? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? Number of Customers d) What is the percentage change of Brand B? Answer in percentage and in 2 decimal places.
4.
The following table shows the arrival data for two airlines in five cities. WANNA GETAWAY HAPPY FLIGHTS Percent On Time Number of Arrivals Percent On Time Number of Arrivals 475 115 102 553 2135 Destination Chicago New York City Seattle Santiago Boston 84.6% 92.8% 88.7% 72.1% 78.8% 745 5355 402 404 233 92.8% 96.3% 91.2% 86.2% 84.1% a. Which airline has the higher percentage of on-time flights when viewed on a per-city basis? Answer: ? b. Compute each of the following percentages. (Simplify and round your answers to one tenth of a percent.) Wanna Getaway Airlines had an on-time percentage of over all five cities. Happy Flights Airlines had an on-time percentage of over all five cities.
Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .
An insurance company calculates car insurance premiums based on the age of the policyholder according to three age groups: Group A consists of drivers younger than 22 years old; Group B consistsof drivers 22—33 years old, and Group C consists of drivers older than 33 years.Its portfolio consists of 10% Group A policyholders, 38% Group B policyholdersand 52% Group C policyholders.The probability of a claim in any 12 month period for a policy belonging to GroupA, B or C is 13%, 3% and 2%, respectively.(i) Calculate the probability that a randomly chosen policy holder from thisportfolio will make a claim during a 12 month period. One of the company’s policyholders has just made a claim(ii) Calculate the probability that the policy holder is younger than 22 years.
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)
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 45 customers per hour, or 0.75 customers per minute. Determine the following operating characteristics for the system. (Round your answers to four decimal places.) (a) The probability that no customers are in the system 1353 (b) The average number of customers waiting 1786 (c) The average number of customers in the system 1.25 (d) The average time (in min) a customer spends waiting 4.2 X min (e) The average time (in min) a customer spends in the system x min 1 (f) The probability that arriving customers will have to wait for service 73 X
A single server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 7 customers per hour and an average service rate of 12 customers per hour. The probability of 2 customers in the system is : a. 0.1418 b. 0.6597 C. 0.4167 d. 0.8582
An insurance company calculates car insurance company calculates car insurance premiums based on the age of the policyholder according to three age groups: Group A consists of drivers younger than 22 years old; Group B consists of drivers 22—33 years old, and Group C consists of drivers older than 33 years.Its portfolio consists of 10% Group A policyholders, 38% Group B policyholders and 52% Group C policyholders. The probability of a claim in any 12 month period for a policy belonging to Group A, B or C is 13%, 3% and 2%, respectively. (i) Calculate the probability that a randomly chosen policy holder from this portfolio will make a claim during a 12 month period. One of the company’s policyholders has just made a claim(ii) Calculate the probability that the policy holder is younger than 22 years.