In England, the most serious emergency calls requesting an ambulanceare classified as 'Red 1'. According to data from NHS England, inMarch 2017, the London Ambulance Service (LAS) received a total of1597 Red 1 emergency calls. Based on this number and adjusting forvariations during the day, suppose that Red 1 calls arriving at the LASin daylight hours may be modelled as a Poisson process with rate 3 perhour.(i1 (2) Calculate and report the probability that three Red 1 callsarrive at the LAS in 30 minutes during daylight hours.(ii) (1) Write down the distribution of the waiting time (in hours)between the arrivals of two successive Red 1 calls at the LASduring daylight hours, including the values ofanyparameters.(2) Calculate and report the probability that the gap between thearrivals of two successive Red 1 calls at the LAS duringdaylight hours will exceed 20 minutes.

Answered: Image /qna-images/answer/b7f346da-3266-4a1a-8056-2d3ec795db7a.jpg

Answered: In England, the most serious emergency…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The manager of a fast-food store realizes that her staffing problems are a result of the variation in the number of customers that arrive at the store. If the same number of customers came each hour, she would know exactly how many servers to have working. It turns out that the Poisson distribution works well to describe the arrivals of customers in any given hour. Explain why the manager has more trouble staffing the store during those hours when the average arrival rate is higher.
Consider the previous question above, A further study determined that cars arrive to this shopping center according to a non-stationary Poisson process. The mean arrival rate increases linearly from 0.17 to 0.49 cars per minute between 10 am and 2 pm. Then the rate remains constant at 0.49 cars per minute between 2 pm and 4 pm. Finally, the rate changes to a constant 0.33 cars per minute between 4 pm and 5 pm. What is the probability that 60 cars will arrive between 1:45 pm and 4:15 pm?
In a certain city, the daily consumption of electricpower in millions of kilowatt-hours can be treated as arandom variable having a gamma distribution with α = 3and β = 2. If the power plant of this city has a daily capacity of 12 million kilowatt-hours, what is the prob-ability that this power supply will be inadequate on any given day?
A small bank has two tellers, one for deposis and one for withdrawals. The service time for each teller is exponentially distributed, with a mean of 1 min. Customers arriving at the bank according to a poisson process, with mean rate 40 per hour; it is assumed that depositors and withdrawers constitute separate poisson processes, each with mean rate 20 per hour , and that no customer is both a depositor and a withdrawer. The bank is thinking of changing the current arrangement to allow each teller to handle both deposits and withdrawals. The bank would expect that each teller's mean service time would increase to 1.2 min, but it hopes that the new arrangement would prevent long lines in front of one teller while the other teller is idle, a situation that occurs from time to time under the current setup. Analyze the two arrangements with respect to the average idle time of teller and the expected number of customers in the bank at any given time.
A suburban hotel derives its revenue from its hotel and restaurant operations. Theowners are interested in the relationship between the number of rooms occupied on anightly basis and the revenue per day in the restaurant. Below is a sample of 25 days(Monday through Thursday) from last year showing the restaurant income and numberof rooms occupied.
Two Poisson processes with rates λ1=6.507and λ2=0.368 resulted from splitting a Poisson process. What is the probability that an arrival from the "parent" process will belong to the second process with rate λ2? Specify your answer to four decimal places.
(a) Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with anaverage of 10 units per hour. The service time is distributed exponentially with a mean of3 minutes. Find the following:i. Average number of units in the system ii. Average waiting time iii. Average length of queue
A large manufacturing company investigated the service it received from its suppliers and discovered that, in the past, 38% of all material shipments were received late. However, the company recently installed a just-in-time system in which suppliers are linked more closely to the manufacturing process. A random sample of 150 deliveries since the just-in-time system was installed reveals that 33 deliveries were late. If we want to test whether the proportion of late deliveries was reduced signicantly at = 0:10 the null and alternative hypotheses are a. Null hypothesis (H0) b. Alternative hypothesis (HA)
A Toy manufacturer has noticed that the number of faulty Toys detected in a production depends on the supervisor on duty and is detected according to a Poisson Process. There are only 2 supervisors: A and B, in the firm. The average number of faulty Toys is 3 per day when A is on duty, while the average number of faulty Toys is 4 per day when B is on duty. quality of one day's production does not have an effect on the next day. B works 4 out of 5 days, while A works 3 out of 5 days. a) What is the probability that no faulty Toys will be produced tomorrow, if B is on duty? b) What is the probability that no faulty Toys will be produced in the next two days? c) Suppose at least one faulty Toy was produced yesterday, what is the probability that A was on duty?
At a toll-booth on-ramp there is a stochastic arrival distribution. Vehicles are counted in 20-second intervals, and vehicle counts are taken in 120 of these time intervals. Based on data collected, no vehicles arrived in 18 of the 120 count intervals. What is the number of the 120 intervals that 3 cars arrived?
If we are watching buses pass by in a Poisson process with buses arriving at the average rate of 10 per hour, then what is the probability (to three decimal place accuracy) that between 3:06pm and 3:24pm we see less than 5 buses?
A real estate agent believes that the value of houses in the neighborhood she works in has increased from last year. To test this claim, she selects random houses in this neighborhood and compares their estimated market value in the current year to their estimated market value in the previous year. Suppose that data were collected for a random sample of 8 houses, where each difference is calculated by subtracting the market value of the previous year from the market value of the current year. Assume that the values are normally distributed. The agent uses the alternative hypothesis Ha:μd>0. Using a test statistic of t≈7.496, which has 7 degrees of freedom, determine the range that contains the p-value. Probability 0.10 0.05 0.025 0.01 0.005 Degrees of Freedom 5 1.476 2.015 2.571 3.365 4.032 6 1.440 1.943 2.447 3.143 3.707 7 1.415 1.895 2.365 2.998 3.499 8 1.397 1.860 2.306 2.896 3.355 9 1.383 1.833 2.262 2.821 3.250 10 1.372 1.812 2.228 2.764 3.169 11…

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