Work-related accidents at a construction site tend to have a Poisson distribution with an average of 1.5 accidents per week.(a) What is the probability that there will be no work-related accidents at this site during a given week? (Round your answer to three decimal places.)0.223(b) What is the probability that there will be at least 1 work-related accident during a given week? (Round your answer to three decimal places.)0.777(c) What is the distribution of x, the number of work-related accidents at this site per month? (Assume there are four weeks in a month.)p(x) =(d) What is the probability that there will be no work-related accidents during a given month? (Assume there are four weeks in a month. Round your answer to three decimal places.)0.0025

From the information, given thatLet X denotes the number of work related accidents at this site per…

Answered: Work-related accidents at a…

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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Empirical research on stock market data for two consecutive trading days indicates that 60% of the stocks that went up on the first day also went up on the second day. Yesterday, 600 stocks went up. Answer the following. (If necessary, consult a list of formulas.) (a) Find the mean of p, where p gives the proportion of the 600 stocks that went up yesterday that will go up today. (b) Find the standard deviation of p. (c) Compute an approximation for P(p <0.58), which is the probability that fewer than 58% of the stocks that went up yesterday will go up again today. Round your answer to four decimal places.
Suppose that the number of traffic accident claims received in a month is modeled by Poisson distribution with intensity λ = 4. Assume that each traffic accident claim takes values $150, $300 or $450 equally likely. Calculate the probability that the total traffic accident claim amounts to exactly $1500.
An IPHONE has an advertised failure rate of 0.01 per hour. The failure rate is constant and the exponential distribution applies. (a) What is the mean time to failure? (b) What is the probability that 300 hours will pass before a failure is observed? (a) The mean time to failure is hours. (Type an integer or a decimal. Do not round.) (b) The probability that 300 hours will pass before a failure is observed is (Round to four decimal places as needed.)
A university is considering setting up an information desk manned by one employee. Based on information obtained from similar information desks, it is believed that people will arrive at the desk at the rate of 18 per hour. It takes an average of 2 minutes to answer a question. It is assumed that arrivals are Poisson and answer times are exponentially distributed. What is the arrival rate? (Include the units.) What is the service rate? (Include the units.) Find the probability that the employee is idle.
Data collected at an airport suggests that an exponential distribution with mean value 2.435 hours is a good model for rainfall duration. (a) What is the probability that the duration of a particular rainfall event at this location is at least 2 hours? At most 3 hours? Between 2 and 3 hours? (Round your answers to four decimal places.) at least 2 hours at most 3 hours between 2 and 3 hours (b) What is the probability that rainfall duration exceeds the mean value by more than 3 standard deviations? (Round your answer to four decimal places.) What is the probability that it is less than the mean value by more than one standard deviation?
In a study, 25,000 adults were randomly surveyed as to the number of grandchildren they have, X. The probability distribution is given below. Find the mean and the standard deviation of the probability distribution using a TI-83, TI-83 Plus, or TI-84 graphing calculator. Round the mean to one decimal place and the standard deviation to two decimal places. x P(x) 0 0.01 1 0.02 2 0.02 3 0.24 4 0.35 5 0.20 6 0.07 7 0.05 8 0.02 9 0.01 10 0.01
Suppose the time it takes for guests to wait for an elevator at the lobby of a certain office building has a uniform distribution between 0 and 4 minutes. What is the probability that, the next time you need to take this elevator, you'll have to wait at most 1.6 minutes? (Your answer should be a decimal. Round to 4 decimal places if necessary.)
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.…
(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?
Please solve (b) only!
Suppose that the annual rate of return for a common biotechnology stock is normally distributed with a mean of 4% and a standard deviation of 4%. Find the probability that the one-year return of this stock will be positive. Round your answer to at least four decimal places. 0 X Ś

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