**Problem 4: Car Wash Modeling with Poisson Distribution**A car wash establishment operates with the number of cars that come per hour, modeled by a Poisson Distribution with a parameter of 6.25.**Task D: Compute the following probabilities:**IV. \( P(8 \text{ cars come in an hour}) \)V. \( P(4 \text{ cars come in an hour}) \)VI. \( P(3 \text{ or fewer cars come in an hour}) \)*Note: For solving these, use the Poisson probability formula:*\[P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}\]*Where \( \lambda \) is the average rate (6.25 in this case), \( k \) is the number of occurrences, and \( e \) is approximately 2.71828.*

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Answered: 4. A Car Wash establishment operates…

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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3) Suppose that in the Bay of Fundy, the mean high tide at a particular harbor is 5.4 m above mean sea level with a coefficient of variation of 20% and assume that this is normally distributed. For simplicity, assume that there are two high tides per day and that a year is made up of twelve 30-day months. a) Determine the asymptotic distribution of the monthly maximum tide height at the harbor (ie. specify the form of the distribution and its parameters). b) Using the results of part (a), derive the corresponding distribution for the 50-year maximum tide height and determine the 50-year most probable maximum tide height.
620A city law-enforcement official has stated that 20% or the items sold by pawn shops within the city have been stolen. Ralph has just purchased 4 items from one of the city's pawn shops. Assuming that the official is correct, and for x = the number of Ralph's purchases that have been stolen, determine the following: a. P(x = 0) c. P(1 s x s 3) b. P(2 s x) d. P(x s 2) %3D
4.4 give the probability data analysis, show solution.
9. Consider a bank office where customers arrive according to a Poisson process with an average arrival rate of customers per minute. The bank has only one teller servicing the arriving customers. The service time is exponentially distributed and the mean service rate is μ customers per minute. It turns out that the customers are impatient and are only willing to wait in line for an exponential distributed time with a mean of 1/μ minutes. Assume that there is no limitation on the number of customers that can be in the bank at the same time. a. Construct a rate diagram for the process and determine what type of queuing system this correspond to on the form A1/A2/A3. b. Determine the expected number of customers in the system when λ = 1 and μ = 2. c. Determine the average number of customers per time unit that leave the bank without being served by the teller when λ = 1 and µ = 2.
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a) The number of students who come into the tutoring center between 8 and 8:30am has a Poisson distribution with λ =5. Determine P(x ≤ 2) b) How many students can the tutoring center be 95% confident that the number of students on any given day will not exceed that number?
A service company receives on average 4 service requests per day. The requests are received randomly according to Poisson process. The company has 2 service engineers and sends one engineer to attend each request. 1 An engineer needs an exponentially distributed service time with the mean of day(s). 2 The company's policy is to have maximum of 2 requests waiting in the queue If this number is reached, all incoming requests are rejected (sent to a competitor). Answer the following questions based on the information provide above: (a) Using the Kendall's notation, indicate what type of queueing system it is: (b) Compute the system state probabilities (provide at least 3 decimals): Po = P1= P2 = P3 = Pa = (c) Compute the expected total number of customer requests (waiting and served) in the system. ELL] = (d) Compute the expected number of accepted requests. Aaccepted = (e) Compute the expected total processing time (waiting + being served) for the accepted requests. E[Time] =
Given: Any network where the critical path is determined by four activities P Q, R, and S; and the early finish for the network is calculated as 12days. Reg'd: a) If the standard deviation value for each of the four critical activitiesis (2/3), calculate the probability of completing the project i)in 14 days; and ii) in 10 days. Value (z) 1.0 1.5 2.0 2.5 Area 0.3413 0.4332 0.4772 0.4938 b) How long would it take to complete this project with 100% certainty?
a) b) c)
Auto vehicles arrive at a petrol pump with one petrol unit in Poisson fashion, averaging 10 units per hour. The service time is distributed exponentially with a mean of 3 minutes. Find the following:a) Average number of units in the systemb) Average waiting time for customersc) The average length of the queued) The probability that a customer arriving at the pump will have to wait.e) The utilization factor for the petrol pumpf) The probability that the number of customers in the system is 2.
A set of n = 5 pairs of X and Y scores has SSX = 18, SSY = 8, ∑X=5, ∑Y=15, SSCP = 3. What is the Pearson Product Moment correlation for these scores? answers: a) 18/12 = 1.50 b) 18/144 = .125 c) 3/12 = .25 d) 3/144 = .21

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4. A Car Wash establishment operates with the number of cars that come per hour to be modeled by a Poisson Distribution with Parameter of 6.25 D. Compute the following: IV. P(8 cars come in an hour) V. P(4 cars come in an hour) VI. P(3 or fewer cars come in an hour)