Calls arrive at a switchboard according to a Poisson process with parameter λ = 5 per hour.(a) In a switchboard, what is the probability that it will be at least 15 minutes till the nextcall?(b) Find the probability that at least seven of the next ten waits between calls will be longerthan 6 minutes.(c) Compute the probability that the first wait shorter than 6 minutes is the next wait.

Given Information: Consider the given information: The calls arrive at a switchboard according to a…

Answered: Calls arrive at a switchboard according…

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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The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. What is the probability that there are no calls within a one-hour interval?
Assume that the number of automobiles arriving at a gasoline station is Poisson distributed and occur at an average rate of 50/hour. The station has only one gasoline pump. If all cars are assumed to require one minute to obtain fuel, what is the probability that a waiting line will occur at the pump?
Q10. Customers arrive in a grocery store according to a Poisson process with rate 6 per hour. What is the probability that exactly one customer has arrived between 9:00 am and 9:20 am? (A) 2e-² (B) 6e-6 (C) 8e-6 (D) 1/3 (E) None of the above
The time between successive calls to a corporate office is exponentially distributed with a mean of 10 minutes. Assume that the times between successive calls are independent of each other. Thus, the calls arrive according to a Poisson process. Determine x such that the probability that there are no calls within x minutes is 0.005.
Roll two fair dice. Use the Poisson approximation to find the probability that you will rollat least one double (meaning both dice land on the same value) in 24 trials. How does this compare tothe exact value? Answer as if explaining to someone.
Customers arrive at a shop according to a Poisson process at a mean rate of 2 customers every ten minutes. The shop opens at 9am. (c) Let Y be the time (in hours) until the 4th customer arrives at the shop. State the distribution of Y and give the value(s) of its parameter(s). (d) Show that the probability of the time until the 4th customer arrives being greater than 15 minutes is 13e-3. (e) Let M be the number of customers who arrive at the shop between 9am and 12 noon. State the distribution of M and give the value(s) of its parameter(s). (f) Calculate P(M = 30) using a normal approximation with the continuity correction.
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A fisherman catches fish according to a Poisson process with rate λ = 0.6 per hour. The fisherman will keep fishing for two hours. If he catches two or more fish after two hours, then he goes home. Otherwise, he continues until he catches a total of two fish (including those caught in the first two hours) and then goes home. (a) Find the probability that he stays for more than two hours. (b) Find the probability that he catches at least three fish. (c) Find the expected number of fish that he catches. (d) Find the expected total fishing time
The number of forklift topples in an area follows a poisson-process with rate 3 accidents per week. Suppose that we observed one forklift topple in the first week. What is the probability that we will observe at most one forklift topples in the next 2 days?
Prob-1 Probability that cars have been assembled in a particular plant as follows: P(plant1) =20%, P(plant2)=24%, P(plant3)=25%, P(plant4)=31%. Total number of cars manufactured by all plants: 1.2 million/year. Number of cars of no warranty claims manufactured by plant1: 223200/year. Compute the warranty claim rate of the cars assembled in plant1? C: warranty Claim rate NC: No warranty claim rate= 1- C P1 20% Total Cars Manufactured C = P2 NC 24% P3 P4 .% 25% 31% C NC C C Z NC .NC
(b) Suppose the number of customers at a Sushi outlet is Poisson distributed where an average of nineteen customers are served per 30 minutes. (i) Over a fifteen-minute period, how many customers are served on average? Find the probability of exactly seven customers served over a fifteen-minute period. Write your answer correct to 4 decimal places. (iii) Calculate the probability at least 1 customer is served over a fifteen-minute period. Write your answer correct to 4 decimal places.
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