Problem 3.On average there are four traffic accidents in a city during one hour of rush-hour traffic. Use the Poissondistribution to calculate the probability that in one such hour there area) No accidentsb) At least five accidents.

3) According to the given information,Mean number of traffic accidents in a city during one hour of…

Answered: Problem 3. On average there are four…

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 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?
Suppose that the following table records the average daily number of traffic accidents reported in the 20 areas of UK. Assuming that the occurrence of traffic accidents in the districts is random and follows the Poisson distribution, estimate the number of districts having various number of traffic accidents on a particular day and complete the table. Number of cases 0 1 2 3 4 >4 Observed number of area 1 4 6 5 2 0 Theoretical probability Estimated number of districts
3
3
5. A distributed system contains 4 computers. What is the probability of its failure in one year, if probability of failure of the computers in this period are 0.1, 0.2, 0.3, 0.4?
1. The distributional pattern of pulmonate slugs inhabiting Libya was studied in the AIUB Journal of Science and Engineering (Aug. 2003). The number of slugs of a certain species found in the survey area was modeled using the negative binomial distribution. Assume that the probability of observing a slug of a certain species (say, Milax rusticus) in the survey area is 0.2. Let Y represent the number of slugs that must be collected in order to obtain a sample of 10 Milax rusticus slugs. a. Give the probability distribution for Y as a formula. b. What is the expected value of Y? Interpret this value.c. Find P(Y = 25).
1. Power companies severely trim trees growing near their lines to avoid power failures due to falling limbs in storms. Applying a chemical to slow the growth of the trees is cheaper than trimming, but the chemical kills some of the trees. Suppose that one such chemical would kill 20% of sycamore trees. The power company tests the chemical on 250 sycamores. Consider this a SRS from the population of all sycamore trees. Calculate the probability that less than 24% of the tress in the sample are killed. (Hint: Shape, Center, Spread, Curve, Calculations, Conclusion....)
10) The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 9.3 tickets per day. Find the probability that exactly four tickets are written on a randomly selected day from this distribution.
5. Based on recent records, the manager of a car painting centre has determined the following probability distribution for the number of customers per day: 1 3 4 P(X = x) 0.05 0.2 0.3 0.25 0.15 0.05 А. f the centre has the capacity to serve three customers per day, what is the probability that one or more customers will be turned away on a given day? В. What is the probability that the centre's capacity will not be fully utilized on a day? С. away is no more than 0.1? By how much the capacity must be increased so the probability of turning customer 2. il
2. The following table shows the income distribution for two groups of people in a country: those who declare to belong to a faith, and those who declare to be free thinkers. Income bracket Middle 13278 2225 Religious outlook Faith believer Free thinker Lower 7940 1241 Upper 4527 813 (a) A person is randomly selected from the group, find the probability that this person is a (i) free thinker. (ii) free thinker given that he/she has middle income. (iii) faith believer or he/she has lower income. (b) Are the events "Free thinker" and "Middle income" independent? Explain your answer. (Note: Round the probabilities to two significant figures)
Example 1 Suppose that the Poisson distribution applies and that the mean number of typographical errors on a single page of a newspaper is 0.5. a) Find the probability that there are no errors on the page? b) Find the probability that there is at least one error on the page? * Laser Pointer 2 Pen 2 Highlighter O Eraser a Erase All Ink on Slide 40:46 ) 1x Ç CC 4+ 144 & %23 3 24 4. 6 8 R T Y. H K NI V. M.
4. Make a “tree” diagram for the following scenario. You go to the corner of State St. and Center Ave and are looking to see if the drivers of the first three cars that pass by you are wearing hats or not wearing hats. a) Generate the probability distribution for problem number 4 assuming that the probability of a driver wearing a hat is 40% and the random variable x is the number of drivers wearing a hat. b) Find the mean, variance and the standard deviation of the probability distribution in part a. Please show all work.

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Problem 3. On average there are four traffic accidents in a city during one hour of rush-hour traffic. Use the Poisson distribution to calculate the probability that in one such hour there are a) No accidents b) At least five accidents.