Q4. A box contains resistors, where 3% of the resistors are deficient because their resistance values are notmeeting specifications written on the box. Technicians of the workshop are testing resistors before the resistorsare soldered to an electrical circuit. The operators select unusable resistor as a deficient one with a probabilityof 0.95. However, the operator can incorrectly check a good resistor and assume that it is a deficient one witha probability of 0.05. If a resistor is selected as deficient after it was tested by an operator, what is theprobability that the resistor is actually unusable for the electrical circuit? (Use Bayes' Formula)

Q4) According to the given information,Probability of the resistor are deficient because their…

Answered: Q4. A box contains resistors, where 3%…

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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Philips Electronics is experimenting with the manufacture of a new type of electric bulb that is very difficult to mass produce at an acceptable quality level. Every hour the Quality Control Manager (QCM) takes a random sample of 6 bulbs produced on the assembly line and tests them for their quality sequentially. Probability that any one bulb is defective is considered to be 0.12. The QCM wants to know the probability of finding 3, 4, or 5. What is the probability of finding 3, 4, or 5 defectives in a random sample of 6 electric bulbs?NOTE: DONOT SOLVE ON EXCEL
A small river is found to be polluted due to the chemical waste from two major industries, A and B. Due to the strict standards enforced by the EPA, the probability of controlling the pollutions from A and B are 0.7 and 0.85, respectively, in the next two years. It is estimated that, if only one of the industries complies with the strict standards of EPA, there is a 75 percent probability of controlling the pollution in the river to an acceptable level. (a) Find the probability of controlling the pollution in the river in the next two years. (b) If the pollution in the river is not controlled in the next two years, what is the probability that it is caused entirely by industry A?
If you play roulettes and bet on 'red' the probability that you win is 18/38 = .4737. People often repeat this between several times. We can consider each time we play a 'trial' and consider it a success when we win, so p = 18/38 or (.4737) and q = 20/38 or (.5263). Suppose that Caryl always places the same bet when she plays roulette, $5 on 'red'. Caryl might play just once, or might play several times. She has a profit (having won $5 more times than she lost $5) if she wins more than half of the games she plays. -when you play 401 times, p is the proportion of those 401 games that you win. You'll profit (winning more than you lose) if you win more than half of your bets p > .5000. c) what is the mean or expected value of p? d) what is the standard deviation of p? e) assume that the distribution of p is Normal and find the probability that Caryl will have a profit if she plays 401 times. show your work or calculator input and round your answer to four decimal places
A new medical test has been designed to detect the presence of a certain disease. Among those who have the disease, the probability that the disease will be detected by the new test is 0.74. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.04. It is estimated that 14 % of the population who take this test have the disease.If the test administered to an individual is positive, what is the probability that the person actually has the disease?
Suppose the sensitivity of a diagnostic procedure to test whether a person has a particular disease is 95 % . A person who actually has the disease is tested for it using this procedure by two independent laboratories. (1) What is the probability that both test results will be positive? (ii) What is the probability that at least one of the two test results willI be positive?
A rapid HIV test that gives results while a client at a clinic waits is unfortunately less accurate than slower lab tests.Applied to people who have no HIV antibodies,one rapid test has probability about 0.004 of producing a false positive.if a clinic tests 200 people who are free of HIV antibodies,what is the chance that at least one force positive will occur?
4. If a randomly chosen athlete tests negative, what’s the probability that the student took a banned substance? Explain why it makes sense for the drug-testing process to be designed so that this probability is less than the one you found in Question 3.5. The district decides to immediately retest any athlete who tests positive. Assume that the results of an athlete’s two tests are independent. Find the probability that a student who gets a positive result on both tests actually took a banned substance. Based on your answer, do you think that an athlete who tests positive twice should be suspended from athletic competition for a year? Why or why not?
A state government hired a contractor for a road-construction project. The contractor's type, its cost efficienciency, is unknown to the government. There is 2/3 probability of the its construction cost being 3 (billion dollars per lane) and 1/3 probability of the cost being 5. More lanes yield more social benefit in the form of faster travel and fewer accidents. The social value V (measured in billions of dollars) from having N lanes on the highway is: V-15N-N?/2. The government is interested in choose N and writing a contract to maximize the benefit to the state (V) net of the fee paid to the contractor (call it F); G-V-F. Your goal as a government official is to design a pair of contracts to separate the types of contractor. You want the contractor to choose "Contract L: Build N lanes and get paid RL dollars" if its cost type is low cost of $3 (billion dollars per lane) and to choose "Contract H: Build NH lanes and get paid RH dollars" if its cost type is high cost $5 (billion…
A particular automatic sprinkler system has two different types of activation devices for each sprinkler head. One type has a reliability of 0.75; that is, the probability that it will activate the sprinkler when it should is 0.75. The other type, which operates independently of the first type, has a reliability of 0.85. If either device is triggered, the sprinkler will activate. Suppose a fire starts near a sprinkler head. (provide your answer in four decimal numbers) (i) What is the probability that the sprinkler head will be activated? (1.5) (ii) What is the probability that the sprinkler head will not be activated? (1.5) (iii) What is the probability that both activation devices will work properly? (1.5) (iv) What is the probability that only the device with reliability 0.75 will work properly? (1.5)
A manufacturer wishes to estimate the accuracy of its final visual inspection process. A random sample of 180 devices is selected from production. An item is defective or “bad” if it contains at least one visually noticeable cosmetic defect. The process improvement team agrees that the sample contains 27 bad items and 153 good items. The team gives the items to a “certified” operator for inspection. The operator rejects 10 good pieces and accepts 11 bad pieces and classifies the remainder correctly. What is the probability that the inspector will reject an item? P(inspector will reject an item) = ________%. Enter value using one decimal place.

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