### Probability and Data Processing: A Case Study of Subcontracted Work**Problem Statement:**An insurance company subcontracts two data processing firms to handle their forms. Firm #1 handles 80% of the forms, while Firm #2 handles the rest. Unfortunately, these firms are run by people and are therefore not perfect. Here are some key details:- It is known that 2% of all forms processed by Firm #1 will be processed incorrectly.- 5% of the forms from Firm #2 will also be processed incorrectly.**Question:**Suppose a random form is chosen from those that have been processed. What is the probability that this form was processed by Firm #2, given that it was processed incorrectly? (Hint: use a probability tree or Bayes' Theorem for the solution.)**Detailed Explanation:**When solving this problem, it's helpful to use Bayes' Theorem, which helps us revise existing predictions based on new evidence. Also, we can use a probability tree to visualize the problem.### Information Recap- Probability a form is handled by Firm #1: P(F1) = 0.80- Probability a form is handled by Firm #2: P(F2) = 0.20- Probability of incorrect processing by Firm #1: P(I|F1) = 0.02- Probability of incorrect processing by Firm #2: P(I|F2) = 0.05Our task is to find the probability that a form was handled by Firm #2 given that it was processed incorrectly, i.e., P(F2|I).### Application of Bayes' TheoremBayes' Theorem formula is:\[ P(F2|I) = \frac{P(I|F2) \cdot P(F2)}{P(I)} \]Where $ P(I) $ is the total probability of a form being processed incorrectly. This can be calculated by summing the probabilities of incorrect processing from both firms:\[ P(I) = P(I|F1) \cdot P(F1) + P(I|F2) \cdot P(F2) \]Substitute the given values:\[ P(I) = (0.02 \cdot 0.80) + (0.05 \cdot 0.20) \]\[ P(I) = 0.016 + 0.

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Answered: their forms. rest. 11) An insurance…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Problem 1P

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(3) Times, Wall Street Journal, and USA Today: In a survey of 150 business travelers, it was found that of three daily newspaper, New York 71 read New York Times; 43 read Wall Street Journal; 34 read USA Today; 30 read New York Times and Wall Street Journal; 25 read New York Times and USA Today; 15 read Wall Street Journal and USA Today; 10 read all three. A person is selected at random from this 150 travelers. (a). What is the probability that the randomly selected person reads New York Times or USA Today but not Wall Street Journal? (b). Given that this traveler read at least one of these three newspapers, what is the probability that he/she read USA Today? (c). Given that this traveler read exactly one of these three newspapers, what is the probability that he/she read Wall Street Journal?
The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 52 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are μ=28.29 and σ=33.493, respectively. Let ?X be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is x¯. Use the central limit theorem (CLT) to determine the probability ? that the mean taxable wages in James' sample of 52 counties will be less than $29…
Cigarette packets used to contain cards representing such things as flowers, film stars or football teams. A complete set would comprise n different cards, say, and collectors would aim to obtain a complete set. Clearly, the first packet bought would contain a new card which would start the collection. The next card obtained might simply duplicate the first card, or it might also be a new card, and add to the collection, and so on. Obtain expressions for the mean and variance of the number of packets which must be purchased until a complete set of cards is obtained.
7. A new drug study was conducted by a drug company. In the study, 10 people were chosen at random to take Vitamin X for 3 months and then have their cholesterol levels checked. In addition, 10 different people were randomly chosen to take Vitamin Y for 3 months and then have their cholesterol levels checked. All 20 people had cholesterol levels between 8 and 10 before taking one of the vitamins. The drug company wanted to see which of the 2 vitamins had the greatest impact on lowering people's cholesterol. The following data was collected: Vitamin X 7.27.5 5.2 6.5 7.7 10 6.47.6 7.77.8 Vitamin Y 4.8 4.44.5 5.1 6.5 8.03.1 4.6 5.2 6.1 (a) Draw a box-and-whisker plot for both sets of data on the same number line. (b) Use the double box-and-whisker plots to compare the 2 vitamins and provide a conclusion for the drug company. (e) State the skewness of both distributions and justify your answer.
A person, Joe, claims to be able to "smell" an illness based on the odor of a person's clothing. Joe is given 12 shirts, each worn by a different person, some of whom had the illness and some of whom did not. The shirts were given to Joe in random order and he had to decide whether each shirt had been worn by an ill patient or by a healthy patient. joe identified 11 of the 12 shirts correctly. If we assume that Joe was just guessing, he would have probability 1/2 of correctly identifying each shirt. Find the probability that Joe would identify AT LEAST 11 shirts correctly by random guessing
An insurance company is thinking about offering discounts on its life insurance policies to nonsmokers. As part of its analysis, the company randomly selects 200 men who are 60 years old and ask them if they smoke at least one pack of cigarettes per day and if they have ever suffered from heart disease. 10 out of the 38 smokers had suffered from some type of heart disease and 12 out of 150 nonsmokers had suffered from some type of heart disease. Can we conclude at the 5% level of significance that smokers have a higher incidence of heart disease than nonsmokers? (Don't hand writing solution)
A doctor wants to determine if a new medication for cholesterol is more effective than the previous medication. The doctor asks her patients if they would like to take part in a study for a new medication, and 30 patients currently taking medication for cholesterol volunteer to participate. Which of the following would be an appropriate procedure for this experiment? The doctor needs to randomly assign 15 patients to the new medication and 15 to the original medication to even out the variability between the patients. The doctor needs to assign the first 15 patients to the new medication and 15 to the original medication to even out the variability between patients. The doctor needs to let the 30 patients choose which medication they are going to take through use of a survey to determine whether they want to participate in the experiment. The doctor needs to randomly assign the 30 patients to the new medication to even out the variability between the patients and to determine if…
The United States Bureau of Labor Statistics (BLS) conducts the Quarterly Census of Employment and Wages (QCEW) and reports a variety of information on each county in America. In the third quarter of 2016, the QCEW reported the total taxable earnings, in millions, of all wage earners in all 3222 counties in America. Suppose that James is an economist who collects a simple random sample of the total taxable earnings of workers in 56 American counties during the third quarter of 2016. According to the QCEW, the true population mean and standard deviation of taxable earnings, in millions of dollars, by county are ?=28.29 and ?=33.493 , respectively. Let ? be the total taxable earnings, in millions, of all wage earners in a county. The mean total taxable earnings of all wage earners in a county across all the counties in James' sample is ?⎯⎯⎯ . Use the central limit theorem (CLT) to determine the probability ? that the mean taxable wages in James' sample of 56 counties will be less than…

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