What is the probability that a person tested as positive of COVID-19 actually having the virus?
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- Find the probability that a lot of 100 items, of which five are defective, will be accepted in a test of a randomly selected sample containing half the lot if, to be accepted, the number of defective items in a lot of 50 cannot exceed one.Show that any uncorrelated Gaussian random variables are statistically independent.Only 6% of people has 0-negative blood type. If a local blood drive has 100 donors, what is the probability that at least 10 of the 100 donors has O-negative blood?
- Assume that hybridization experiments are conducted with peas having the property that for offspring, there is a 0.25 probability that a pea has green pods. Assume that the offspring peas are randomly selected in groups of 40. What is the meanA new vaccine against the coronavirus has been developed. The vaccine was tested on 10,000 volunteers and the study has shown that 65% of those tested do not get sick from the coronavirus. Unfortunately, the vaccine has side effects and in the study it was shown that the probability of getting side effects among those who did not get sick is 0.31, while the probability of getting side effects among those who got sick from corona despite vaccination is 0.15. (a) Draw an event tree and show on the event tree all the probabilities in branch points.Physicians at a clinic gave what they thought were drugs to 960960 asthma, ulcer, and herpes patients. Although the doctors later learned that the drugs were really placebos, 5252 % of the patients reported an improved condition. Assume that if the placebo is ineffective, the probability of a patients condition improving is 0.490.49. For the hypotheses that the proportion of improving is 0.490.49 against that it is >0.49>0.49, find the p-value. p=p=
- A G's production of 950 manufactured parts contains 70 parts that do not meet the customer requirements . Two parts are selected randomly without replacement from the batch. What is the probability that the second part is defective given that the first part is defective?According to the CDC, as of MAY 2021, it is suspected that 2% of the US population currently have active coronavirus. According to Johns Hopkins, a particular type of COVID test (RT-PCR), has a false negative rate of 20%. That is, if a person has COVID, and takes this test, there is a 20% chance of testing negative. The false positive rate is about 5%. That means that about 5% of people who don't have COVID will nonetheless test positive. Consider the following two-way table for 10,000 randomly selected people who were tested for COVID using (RT-PCR). Positive test Negative test Total Has COVID A 40 200 No COVID 490 B 9800 Total 10000 1. fill in the missing values in the table. A • B • C • D 2. What is the probability of choosing someone who tested positive? 3. What is the probability of choosing someone who has COVID? 4. What is the probability of choosing someone who does not have COVID and tested positive? 5. What is the probability of choosing someone with COVID given that they…Results from a Chembio test for hepatitis C among HIV-infected patients (based on data from a variety of sources) showed 337 subjects with positive test results including 2 false positive results. There were 1,163 negative results, including 10 false negative results. What is the probability that a randomly selected subject has a positive test result given he has no hepatitis C ?
- In a certain population, 11% of people are infected by a certainvirus. A virus detection test correctly detects 94% of cases in whichindividuals are infected, but mistakenly assigns 6% of positive resultsfor the uninfected (false positives). How likely is it that a person's testof this population give a positive result?Find the probability that a lot of 100 items, of which five are defective, will be accepted in a test of a randomly selected sample containing half the lot if, to be accepted, the number of defective items in a lot of 50 cannot exceed one.In a study of 213,270 cell phone users, it was found that 77 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is a 0.000397 probability of a person developing cancer of the brain or nervous system. We therefore expect about 85 cases of such cancer in a group of 213,270 people. Estimate the probability of 77 or fewer cases of such cancer in a group of 213,270 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous system? (a) P(x ≤ 77) = (Round to four decimal places as needed.)
