If the odds in favor of E occurring are 4 :7, then find P(E) and P(E'). P(E) =(Type an integer or a simplified fraction.) P(E')=(Type an integer or a simplified fraction.)
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- Two processes are used to produce forgings used in an aircraft wing assembly.Of 200 forgings selected from process 1, 12 do not conform to the strength specifications,whereas of 300 forgings selected from process 2, 6 are nonconforming.Test the hypothesis that the two processes hava identical fractions nonconforming.Use a=0.05 and explain the result.A forest consists of two types of trees; young (between 0 and 3 m tall) and adults (more than 3 m). Each year, 20% of young trees die, 10% sell for $20 each, 30% remain between 0 and 3 m, and 40% grow taller than 3 m. Each year, 40% of adult trees sell for $50, 20% sell for $20, 30% remain in the forest, and 10% die. What percentage of the trees planted sell for $50?A park ranger is searching for bears in a region of the park where on average there are 5 bears per square mile. The bears are solitary independent creatures, so it is reasonable to assume that the numbers of bears in disjoint regions are independent unknowns and that the number expected in any region is proportional to the area of the region. The ranger can also assume that in a very tiny region, say a square inch, it is impossible to find more than one bear. What is the probability (two decimal place accuracy) that he finds less than 12 bears in a given 2 square mile region of the park?
- If the odds of catching the flu among individuals who take vitamin C is 0.0342 and the odds of catching the flu among individuals not taking vitamin C is 0.2653, then the individuals not taking vitamin C are 7.7573 times more likely to catch the flu than individuals taking vitamin C.A die is weighted so that the probability of a 1 is 0.2, the probability of a 2 is 0.2, the probability of a 3 is 0.2, the probability of a 4 is 0.1, the probability of a 5 is 0.2, and the probability of a 6 is 0.1. An experiment consists of rolling the die until the total sum of all the dice rolled is greater than or equal to 3. If YY is the number of times the die is rolled, how many distinct values of YY are possible? Part 2 Find the probability density function of YY (Note: Please write the values of YY in ascending order! Value of X ProbabilityWhen doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial samples of different blood specimens. If samples from four people are combined and the mixture tests negative, we know that all four individual samples are negative. Find the probability of a positive result for four samples combined into one mixture, assuming the probability of an individual blood sample testing positive for the virus is 0.04.
- Suppose that there are 4 deaths due to stomach can- cer among workers in a tire plant from 1/1/64 to 12/31/83, while 2.5 are expected based on U.S. mortality rates. Provide a 95% CI for the expected number of deaths from stomach cancer over 20 years among the tire workers. Is the number of cases of stomach cancer excessive?Suppose a single die is rolled 10 times. What is the probability of rolling a one, three ormore of the 10 times? Show all your work using fractions and answer with a reduced fraction.Do not use any decimals. DO NOT USE P VALUE TO ANSWER THE QUESTION.4. Using the law of total probability with disease prevalence of 0.001 calculate the probability that a randomly chosen person from the population tests negative for the disease. 5. Using the law of total probability with disease prevalence of 0.001 calculate the probability that a randomly chosen person from the population tests positive for the disease. 6. Using Bayes’ formula with disease prevalence of 0.001, find the probability that a patient who tested negative is healthy.
- Two different types of injection-moulding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discoloured. Two random samples, each of size 300, are selected, and 13 defective parts are found in the sample from machine 1, and 8 defective parts are found in the sample from machine 2. Is it reasonable to conclude that both machines produce the same fraction of defective parts, using α = 0.05, find the value of zcalc? Please report your answer upto 2 decimal places.The police tested 550 people, to see if anyone would match the partial fingerprint at the crime scene. The probability of getting a false-positive result for a single person, was 0.3%. Using the same formula and method as shown in the video: What would be the new approximate percentage probability of getting at least one false-positive result, if 550 people are still tested, but the probability of getting a false-positive result for a single person was 0.4% instead of 0.3% ? (Assume all other aspects of the situation are the same as in the original problem, with the only change being the probability of getting a false-positive result for a single person.) Round to four digits past the decimal point, and include a percentage symbol in your answer (with no spaces).In a clinical study, a random sample of 540 participants agree to have their blood drawn, which is to be examined for the presence of antibodies against a certain contagious disease. It is found in 22% of the blood samples, which experimenters hope to extrapolate to the general population. From this random sample, 10 participants' blood samples are selected at random. If X is the number of samples out of the 10 who have these antibodies, what can we say about X? A. The sample size is not large enough for us to approximate X using a normal distribution B.The expected value of X is 22 C. X can be approximated using a normal distribution in lieu of a binomial distribution D. X has a sampling distribution that is normal