5.A church opens at 8:00am on Sunday. The number of visitors entering the churchin a minute follows a Poisson distribution with a mean of 1.8.(a) What is the variance of the number of visitors entering the church in aminute.(b) Find the probability that 3 visitors entering the church in the first twominutes after the church opens.(c) At 8:00, only one door at the entrance of the church is opened. If in any twoconsecutive minutes, there are at least 4 visitors entering the church in eachminute, then a second door will be opened. Find the probability that thesecond door is just opened three minutes after the church opens.

Given: The number of visitors entering the church in a minute follows a Poisson distribution with…

Answered: A church opens at 8:00am on Sunday. The…

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 mean number of customers arriving at a service station during the 25-minute period is 5. Find the probability that 3 or more customers will arrive at the service station during a 25-minute period. Assume that the service system can be modeled as a Poisson distribution
E The number of accidents occurring in a plant in a month follows Poisson distribution with mean as 5.2. The probability of occurrence of less than 2 accidents in the plant during a randomly selected month is
Suppose people immigrate into a territory at a Poisson rate of 2 per day. Assume that 40% of immigrants are adults and 60% are kids. a. What is the probability that 4 adult immigrants arrive in the next 3 days? b. What is the probability that the time elapsed between the arrival of 24th and the 25th kids is more than 2 days? c. Find mean and the variance of the time needed to have 50 adult immigrants in the territory.
A petrol pump station has 4 pumps. The service times follow the exponential distribution with a mean of 6 minutes and cars arrive for service in a Poisson process at the rate of 30 cars per hour. (i) What is the probability that an arrival would have to wait in line?(ii) Find the average waiting time, the average time a car spent in the system and the average number of cars in the system. (iii) For what percentage of time would a pump be idle an an average?
The number of typing errors made by a typist has a Poisson distribution with an average of three and a half errors per page. If five or more errors appear on a given page, the typist must retype the whole page. What is the probability that the typist makes 3 errors on a page? What is the probability that a randomly selected page does not need to be retyped?
Hits to a high-volume website are assumed to follow a Poisson distribution with a mean of 1200 per day. What is the probability that the number of hits to the website tomorrow will be between 1190 and 1220 (inclusive)?
An online advertisement is viewed 1.1 times per hour an average. The number of views per hour follows a Poisson distribution. Find the probability that the advertisement will be viewed more than 2 times in a randomly selected hour. (Provide your answer as a number between 0 and 1 rounded to 3 decimal places.)
The number of goals scored at state college hockey games follows as poisson distribution with a mean of five goals per game. Find the probability that a randomly selected state college hockey game would have more than three goals
Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation, according to a General Accounting Office study completed in response to a congressional request. The accident rate for small aircraft in the 11 mountainous western states is 2.4 accidents per 100,000 flight operations. (a) Let r = number of accidents for a given number of operations. Explain why the Poisson distribution would be a good choice for the probability distribution of r. Frequency of accidents is a rare occurrence. It is reasonable to assume the events are independent.Frequency of accidents is a common occurrence. It is reasonable to assume the events are independent. Frequency of accidents is a common occurrence. It is reasonable to assume the events are dependent.Frequency of accidents is a rare occurrence. It is reasonable to assume the events are dependent. (b) Find the probability of no accidents in 100,000…
(c) Does this Poisson distribution provide a good model for the number of accidents in this example (as per Table 1)? Explain why or why not. Use R to produce a graph to help support your answer (produce the R as part of your answer). (d) Use the model in (b) to estimate the probability that less than 2 accidents were recorded in any randomly chosen week. How does this compare to the actual data?

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