Q2)Suppose that for the general population, 1 in 10000 people carries the human immunodeficiencyvirus (HIV). A test for the presence of HIV yields either a positive (+) or negative (-) response. Ifthe person has HIV the test correctly yields a positive (+) with probability 0.98. Similarly, if theperson does not have HIV the test yields a negative (-) with probability 0.97. What is P[H|+],the conditional probability that a randomly chosen person has the HIV virus given that the persontests positive?

Bayes' theorem is a fundamental principle in probability theory that describes the relationship…

Answered: Suppose that for the general…

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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The statement below is true/false: A type II error is defined as rejecting H1 when it is true. Producers’ risk in rejecting product with good quality is a type I error. Power of a test is the probability of accepting H0 when it is false
The reported rate for colorblindness for men ages 65 and older is 12%. Assume this estimate is the true population proportion of men ages 65 and older. A SRS of 25 men ages 65 and older is taken. Calculate the probability that proportion of men ages 65 and older who have colorblindness is more than 0.10. A. 3783 B. 6217 C. This can’t be done because np is not greater than D. This can’t be done because n is not greater than 30 and we are not told that the variable is normally distributed.
In a particicular second hand store, 9 of the 42 cell phones sold will have some sort of a defect. If you randomly select two cell phones to purchase, what is the probability that BOTH of them have a defect?NOTE: this is a case of WITHOUT REPLACEMENT, since once you select one, that can't be chosen again for your second pick.(Give answer as a decimal correct to four decimal places.)probability =
According to recent reports, currently 39% of the population of NC (adults and children) has been fully vaccinated against Covid. Suppose of random sample of 400 individuals from the population of NC is selected. Let x represent the number in the sample who are fully vaccinated. d. Find the probability that 130 or fewer in the sample have been fully vaccinated. Round to 4 decimal places. Would this result be unusual? Explain.
The probability of a randomly selected adult in one country being infected with a certain virus is 0.006. In tests for the virus, blood samples from 25 people are combined. What is the probability that the combined sample tests positive for the virus? Is it unlikely for such a combined sample to test positive? Note that the combined sample tests positive if at least one person has the virus. a. The probability that the combined sample will test positive is (Round to three decimal places as needed.)
A study completed in 2018 found that approximately 1 out of every 20 people have walked out of a restaurant without paying the bill (the dine and dash). A random sample of 150 people is collected. a. What is the probability that more than 10% of them have walked out of a restaurant without paying?P( p̂ > 0.1)= b. What is the probability that less than 3% of them have walked out of a restaurant without paying?P( p̂ < 0.03)= c. What is the probability that between 5% and 10% of them have walked out of a restaurant without paying?P(0.05 < p̂ < 0.1)=
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.…
Let’s assume that the “prevalence” (i.e., the proportion of infected people) of COVID-19 in a particular area is 5%. Tests are randomly administered in this area (i.e., regardless of whether a person is symptomatic or not). The test has a 1% false positive rate and a 4% false negative rate. If a person tests positive, what is the probability that he or she is actually infected with COVID-19?

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