Medical researchers developed a test that determines whether a person has a particular disease. The results have produced the following probabilities, where Drepresents having the disease and N represents a negative test.P(D'IN) = 0.85 and P(D|N') = 0.74. Assuming that P(N') = 0.09, find P(N'|D).%3DP(N'|D) =(Round to the nearest thousandth as needed.)

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Answered: Medical researchers developed a test…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Suppose that one chemical plant in a large corporation is accused of exceeding the established limits of toxins being released into the atmosphere. A decision is made to test whether or not the mean level of toxins exceeds the tolerance level μ0=100μ0=100 ppm (parts per million). How would the null and alternative hypotheses be set up given that the researcher is working for the corporation? How would those hypotheses change if the researcher is working for the Environmental Protection Agency (EPA)?
Medical researchers developed a test that determines whether a person has a particular disease. The results have produced the following probabilities, where D represents having the disease and N represents a negative test. P(D'IN) = 0.85 and P(DIN') = 0.72. Assuming that P(N") = 0.12, find P(N'|D). P(N'|D) =O (Round to the nearest thousandth as needed.)
Anomal distribution has of mu = 50 with sigma = 6 6. one score randomly selected from this distributionwhich is the probability that the score will be greater than X = 46
10. A sample of high-capacity resistors is tested until failure and the results fitted to a Weibull probability model. Based on these tests, the reliability function of a resis- tor is estimated to be -0.0013 rl.83 R(1) = e' a. What is the failure rate function for these resistors? b. Is this resistor more likely to fail as it ages? c. What is the probability that a resistor will function for more than 30 hours with- out failure? d. Suppose that a resistor has been operating for 50 hours. What is the probability that it fails in the 5 1st hour? [Use the results of part (a) for your calculations.]
Consider the problem of diagnosing a rare disease. Let’s say the occurrence of thisdisease is one in a thousand i.e. P(D = +) = 0.001. There is a test T which correctlyidentifies the disease 99.9% of the time, i.e. P(T = +|D = +) = 0.999. However, italso has a false positive rate of 0.02, i.e. P(T = +|D = −) = 0.02 i. If a random person from the population is tested, what is the probability they willreceive a positive test, i.e. P(T = +)? ii. Given that the test is positive, what is the probability that the person has the disease,i.e. P(D = +|T = +)?
Question 7 According to the data, the weight of a randomly selected checked-in luggage has a normal distribution with a mean of 51 lbs and a standard deviation of 9 lbs. Let X be the weight of a randomly selected checked-in luggage and let S be the total weight of a random sample of size 33. 1. Describe the probability distribution of X and state its parameters and o: X~ Select an answer (μ = Select an answer unknown X² B N T 2. Use the Central Limit Theorem and find the probability that the weight of a randomly selected checked-in luggage is less than 61 lbs. (Round the answer to 4 decimal places) Check-In Select an answer Select an answer the original population is normally distributed the sample size is large (n>30) although the distribution of the original population is unknown the sample size is small (n<30) and the distribution of the original population is unknown the distribution of the original population is unknown S~ Select an answer (s= Select an answer σ= to describe the…
The table shows the results of a restaurant survey. Find the probability P(Y'IC'). Service Great Meal Lunch (X) Dinner (Y) Total 4247 (A) Service Good (B) Service Okay (C) Service Poor Total (D) 32 47 14 45 45 47 14 43 77 94 28 88 80 138 149 287 P(Y'|C')= (Simplify your answer. Type an integer or a simplified fraction.)

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