1 For each of the following binomial distributions, use the binomial formula to calculate P(X= 3)....
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1 For each of the following binomial distributions, use the binomial formula to calculate P(X= 3). Give your answers to 6 significant figures. In each case use an appropriate Poisson approximation to find P(X= 3); again give your answers to 6 significant figures and calculate the percentage error in using this approximation. Describe what you notice. il X-B(25,0.2) (ii) X-B(250, 0.02) (ii) X-B(2500, 0.002) An automatic machine produces washers, 3% of which are defective according to a severe set of specifications. A sample of 100 washers is drawn at random from the production of this machine. Using a suitable approximating distribution, calculate the probabilities of observing lil exactly 3 defectives lil between 2 and 4 defectives inclusive. 3 The number of civil lawsuits filed in state and federal courts on a given day is 500. The probability that any such lawsuit is settled within one week is 0.01. Use the Poisson approximation to find the probability that, of the original 500 lawsuits on a given day, the number that are settled within a week is li exactly seven liil at least five fiil at most six. One per cent of the items produced by a certain process are defective. Using the Poisson approximation, determine the probability that in a random sample of 400 articles (il exactly five are defective at most five are defective. 5 Betty drives along a 50-kilometre stretch of road five days a week, 50 weeks a year. She takes no notice of the 70 kmh-1 speed limit and, when the traffic allows, travels between 95 and 105 kmh-1. From time to time she is caught by the police and fined but she estimates the probability of this happening on any day is. If she gets caught three times within three years she will be disqualified from driving. Use Betty's estimates of probability to answer the following questions. What is the probability of her being caught exactly once in any year? f) What is the probability of her being caught less than three times in three years? What is the probability of her being caught exactly three times in three years? 1 For each of the following binomial distributions, use the binomial formula to calculate P(X= 3). Give your answers to 6 significant figures. In each case use an appropriate Poisson approximation to find P(X= 3); again give your answers to 6 significant figures and calculate the percentage error in using this approximation. Describe what you notice. il X-B(25,0.2) (ii) X-B(250, 0.02) (ii) X-B(2500, 0.002) An automatic machine produces washers, 3% of which are defective according to a severe set of specifications. A sample of 100 washers is drawn at random from the production of this machine. Using a suitable approximating distribution, calculate the probabilities of observing lil exactly 3 defectives lil between 2 and 4 defectives inclusive. 3 The number of civil lawsuits filed in state and federal courts on a given day is 500. The probability that any such lawsuit is settled within one week is 0.01. Use the Poisson approximation to find the probability that, of the original 500 lawsuits on a given day, the number that are settled within a week is li exactly seven liil at least five fiil at most six. One per cent of the items produced by a certain process are defective. Using the Poisson approximation, determine the probability that in a random sample of 400 articles (il exactly five are defective at most five are defective. 5 Betty drives along a 50-kilometre stretch of road five days a week, 50 weeks a year. She takes no notice of the 70 kmh-1 speed limit and, when the traffic allows, travels between 95 and 105 kmh-1. From time to time she is caught by the police and fined but she estimates the probability of this happening on any day is. If she gets caught three times within three years she will be disqualified from driving. Use Betty's estimates of probability to answer the following questions. What is the probability of her being caught exactly once in any year? f) What is the probability of her being caught less than three times in three years? What is the probability of her being caught exactly three times in three years?
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Applied Regression Analysis and Other Multivariable Methods
ISBN: 978-1285051086
5th edition
Authors: David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg
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