(b)Suppose that a distribution of the number of workers per year that will absent fromwork per year is a Poisson random variable with 2 = 5.(i)Compute the probability that at most 3 worker per year will absent from work?(ii)Compute the probability that more than 1 worker per year will absent fromwork?

Answered: Image /qna-images/answer/193a17be-50e5-43e0-864a-d208769d03d4.jpg

Answered: Suppose that a distribution of the…

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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A player will win if he rolls two dies and gets a sum equal to 6. If he plays 12 times, what is the probability that he gets at least 2 wins? b) Suppose that the number of customers that enter a bank in an hour is a Poisson random variable, and suppose that P(X =0) = 0.02. i. What is the probability that at most one person enter the bank in one hour? ii. Determine the mean and standard deviation of X
Suppose that telephone calls arriving at a particular switchboard follow a Poisson process with an average of 4 calls coming per minute. What is the probability that up to a minute will elapse by the time 2 calls have come to the switchboard using the Gamma distribution? What is the probability that less than 30 seconds will elapse between successive calls coming to the switchboard? What is the probability of having at least 3 calls arrive to the switchboard in one minute? What is the probability of having at most 9 calls arrive to the switchboard in three minutes?
Suppose that the test score of a student taking the final of a probability course is a random variable with mean 80. (a) Give an upper bound for the probability that a student's test score will exceed 90. P{score > 90} < (b) Suppose that we know, in addition, that the variance of students' test scores on the final is 30. What can you say about the probability that a student will score between 70 and 90 (do not use the central limit theorem)? P{70 < score < 90} ? (c) How many students would have to take the final to ensure with a probability of at least 0.95 that the class average would be within 3 of 80 (do not use the central limit theorem)? n = (d) If you use the central limit theorem in (c), what is your estimate for the number of students needed? п —
The number of clients arriving at a bank machine is Poisson distributed with an average of 2 per minute. For a 5-minute period, Find the expected value and standard deviation. What is the probability that 2 customers will arrive in a 5-minute period? What is the probability that no more than 2 customers will arrive in a 5-minute period? What are the underlying assumptions that allow us to consider this phenomenon as a Poisson distribution?
The expected life of a certain component in a mechanism is treated as a random variable having a gamma distribution with a = 3 and ß = 2. The average expected life of such component is 12 months, what is the probability that this component can have a greater than average expected life?
Let E and F be two events of an experiment with sample space S. Suppose P(E) = 0.46, P(F^) = 0.65, and P(E U F) =0.7. Calculate the probabilities below. (a) P(E) = (b) P(F) (c) P(E n F) =
What type of distribution is appropriate to model the time between two consecutive departures from the gate of an airport Poisson Binomial Exponential Geometric
Chains "A" and "B" are made of the same steel. "A" consists of three links and "B" consists of six links, each link having a normal distribution function of the resisting strength with a mean of 60,000 psi and standard deviation of 5,000 psi. Determine which chain is generally weaker (from a probabilistic point of view) by plotting the probability distribution functions of their resisting strengths on the same diagram.
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days. (a) In words, define the random variable X. Edit Insert - Formats - B A く) (b) Find the ZSCore for a trial lasting 20 days. (Round your answer to three decimal places.) (c) If one of the trials is randomly chosen, find the probability that it lasted at least 20 days. (d) Shade the area corresponding to this probability in the graph below. (Hint: The x-axis is the z-score. Use your z-score from part (b), rounded to one decimal place).
Assume that arrivals of cars at a gas station can be modeled by a Poisson process with rate 2 cars per hour. What is the probability that one has to wait at least 3 hours for the arrival of 3 cars?
Data from 14 cities were combined for a 20-year-period, and the total 280 city-years included a total of 168 homicides. After finding the mean number of homicides, find the probability that a randomly selected city has the followng number of homicides. Homicides each city-year: 0, 1, 2, 3, 4 Actual results: 155, 90, 28, 6, 1 P(0)=
A random sample of 300 employees was chosen to take COVID-19 test. Results indicated that 180 employees have positive results. Use a 0.05 significant level. Set up the appropriate hypotheses that attempt to test the claim most employees at the company have COVID-19 O a. HO:P3D0.5 and Hl:p>=0.5 HO: p=0.5 and Hl: p0.5 Od. HO: p-0.5 and HT: p<0.5 e. None of these alternatives is correct.

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