A chemical engineer is interested in determining whether a certain trace impurity is present in a product.An experiment has a probability of .80 of detecting the impurity if it is present. The probability of notdetecting the impurity if it is absent is .90. The prior probabilities of the impurity being present andbeing absent are .40 and .60, respectively. Three separate experiments result in only two detections.What is the posterior probability that the impurity is present?

Answered: Image /qna-images/answer/b9d2a129-9c51-4ac5-86ec-1e7badbdc88f.jpg

Answered: A chemical engineer is interested in…

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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Suppose a lung cancer test is 85% sensitive and 93% specific. That is, the test will produce 85% true positive results for those with lung cancer and 93% true negative results for those without lung cancer. Suppose that 3.2% of people actually have lung cancer. If a randomly selected individual tests positive, what is the probability he or she does not have cancer? YOUR ANSWER SHOULD BE BETWEEN O AND 100 AND ROUNDED To 4 DECIMAL PLACES. (e.g. 59.5321 would be 59.5321%)
A pair of dice is rolled, and the larger of the two numbers showing is recorded. Find the expected value of this experiment.
Many fire stations handle emergency calls for medical assistance as well as calls requesting firefighting equipment. A particular station says that the probability that an incoming call is for medical assistance is 0.84. This can be expressed as P(call is for medical assistance) = 0.84. (a) Give a relative frequency interpretation of the given probability. O Eighty-four percent of all calls to the station are for medical assistance. O None of the calls to the station are for medical assistance. O Sixteen percent of all calls to the station are for medical assistance. O All calls to the station are for medical assistance. O Fifty percent of all calls to the station are for medical assistance. (b) What is the probability that a call is not for medical assistance?
An airline is considering adding a route to the city of Buffalo, NY. Market research predicts that if the airline serves Buffalo, there is a 32% probability of making a $500,000 profit, a 22% chance of breaking even, and a 46% probability of losing $300,000. What is the expected value of adding a route to Buffalo?
A market research company is interested in the home owership rates across Melbourne suburbs. They survey 253 households in the suburb of Carlton where the true probability of being a home owner for a given household is 0.782. Assume that the home ownership status of each households is independent of others. What is the expected value of the variable X, defined as the number of people who own homes in the sample (round to the nearest number of people).
A factory uses a specific machine to produce pieces. From previous data, we know that 97% of the time the machine is set up correctly. If this is the case, it produces 95% acceptable (non-defective) pieces. However, if it is not set up correctly, it produces only 40% of acceptable pieces Q23 Given that the selected piece is non-defective, what is the probability that the machine is set up correctly? Your answer should be in % and have two digits after the period. So, if your answer is 50.023%, enter 50.02. Your Answer:
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)
pls answer no.3 on paper
Use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion. A study of the effect of seatbelt use in head-on passenger car collisions found that drivers using a seatbelt had a 64.1% survival rate, while drivers not using a seatbelt had a 41.5% survival rate. If seatbelts have no effect on survival rate, there is less than a 0.0001 chance of getting these results. What do you conclude? The probability shows that the sample results ▼ could could not have easily occurred by chance. It appears that there ▼ is is not sufficient evidence to conclude that seatbelts do have an effect on survival rate.

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