Yhmeer is watching a shower of meteors (shooting stars). During the shower, he sees meteors at an average rate of 1.3 per minute. (a) State the conditions required for a Poisson distribution to be a suitable model for the number of meteors which Yhmeer sees during a randomly selected minute (b) Using Excel or otherwise, determine the probability that, during one minute, Yhmeer sees (i) exactly one meteor (ii) at least 4 meteors

Yhmeer is watching a shower of meteors (shooting stars). During the shower, he sees meteors at an average rate of 1.3 per minute. (a) State the conditions required for a Poisson distribution to be a suitable model for the number of meteors which Yhmeer sees during a randomly selected minute (b) Using Excel or otherwise, determine the probability that, during one minute, Yhmeer sees (i) exactly one meteor (ii) at least 4 meteors

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Description: Yhmeer is watching a shower of meteors (shooting stars). During the shower, hesees meteors at an average rate of 1.3 per minute.(a) State the conditions required for a Poisson distribution to be a suitable modelfor the number of meteors which Yhmeer

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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Person P is walking with his dog every day. He decides to model the time intervals between dog encounters (i.e., how long does it take between two encounters) with the independent random variables Y1, . . ., Yn. Number of dogs encounters per day, the number of customers entering a store per hour, the number of bacteria per liter of water, etc. are classically modelled using the Poisson distribution. With an exponential distribution, on the other hand, is used for modelling intervals of between events and how long a light bulb lasts, for example. After learning this, person P decides to model the observations in such a way that the corresponding random variables Y1,..., Yn for a random sample, that is, independent observation, of the exponential distribution Exp(1/µ), µ > 0. The parameter μ > 0 is used as the statistical model parameter 1 which is the expected value of each observation random variable Yi. Derive (a) the joint density function f(y;µ) specifying the model. (b) the…
Part b is: What is the probability that a company selected at random will have allocated to environmental and pollution control a proportion that exceeds the population mean given in (a)?
The number of requests for assistance received by a towing service is a Poisson process with rate a = 10 per hour. (a) Compute the probability that exactly thirteen requests are received during a particular 2-hour period. (Round your answer to three decimal places.) (b) If the operators of the towing service take a 30 min break for lunch, what is the probability that they do not miss any calls for assistance? (Round your answer to three decimal places.) (c) How many calls would you expect during their break?
Adult men's heights (in inches) are normally distributed with μ = 70 and σ = 3. Adult women heights (in inches) are normally distributed with μ = 67 and σ = 2. Members of the "Beanstalk Club" must be at least six feet (72 inches) tall. (a) If a man is selected at random, what is the probability that he is eligible for the Beanstalk Club? (b) If a woman is selected at random, what is the probability that she is eligible for the Beanstalk Club?
The number of traffic accidents at a certain intersection follows a Poisson distribution with A=2 per year. Let X be the number of accidents that occur in a 4-year period. Do not round your intermediate computations. Round your final answers to four decimal places. (a) Find P (8). (b) Find P(Less than 3). (c) Find P(More than 4). Part 1 of 3 P(8)= Part 2 of 3 P(Less than 3)= Part 3 of 3 P(More than 4)=
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.
The average number of collisions in a week during the summer months at a particular intersection is 2. Assume that the requirements of the Poisson distribution are satisfied. What is the probability that there will be exactly one collision in a week?
Some previous studies have shown a relationship between emergency-room admissions per day and level of pollution on a given day. A small local hospital finds that the number of admissions to the emergency ward on a single day ordinarily (unless there is unusually high pollution) follows a Poisson distribution with mean = 2.0 admissions per day. Suppose each admitted person to the emergency ward stays there for exactly 1 day and is then discharged. The hospital is planning a new emergency-room facility. It wants enough beds in the emergency ward so that for at least 95% of normal-pollution days it will not need to turn anyone away. What is the smallest number of beds it should have to satisfy this criterion? Answer the previous question for a random day during the year.
The number of requests for assistance received by a towing service is a Poisson process with rate a = 4 per hour. (a) Compute the probability that exactly ten requests are received during a particular 2-hour period. (Round your answer to three decimal places.) (b) If the operators of the towing service take a 30 min break for lunch, what is the probability that they do not miss any calls for assistance? (Round your answer to three decimal places.) (c) How many calls would you expect during their break? You may need to use the appropriate table in the Appendix of Tables to answer this question.
Question 4In a reality program show, it has been studied that Mawi’s winning votes are according toa Poisson distribution with 5 votes per minute. Meanwhile, Siti’s winning votes arefollowing the Poisson distribution with 4.5 votes per minute.(a) Calculate the probability that Mawi wins 5 votes or more within three minutes.(b) Within 1 hour of the program, calculate the probability that Siti wins more than300 votes.[Hint: use normal approximation to solve the question](c) After two hours running of the reality program, using the normal approximationand assuming that Mawi’s votes and Siti’s votes are mutually independent, find theprobability that total Siti’s votes is higher than Mawi’s.
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…
The number of requests for assistance received by a towing service is a Poisson process with rate a = 4 per hour. (a) Compute the probability that exactly thirteen requests are received during a particular 2-hour period. (Round your answer to three decimal places.) (b) If the operators of the towing service take a 30 min break for lunch, what is the probability that they do not miss any calls for assistance? (Round your answer to three decimal places.) (c) How many calls would you expect during their break? You may need to use the appropriate table in the Appendix of Tables to answer this question.