A worn machine is known to produce 10% defective components. In a run of 3 components, find the probabilities that of 0, 1, 2 and 3 defectives using both the Binomial and the Poisson. Comment on your results
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- Suppose that you are taking a multiple-choice exam with five questions, each have five choices, and one of them is correct. Because you have no more time left, you cannot read the question and you decide to select your choices at random for each question. Assuming this is a binomial experiment, calculate the binomial probability of obtaining exactly one correct answer.A huge pencil bag contains 40 pencils of two different shades, 4B and 6B. Initially, there are x numbers of 6B pencils in the bag. If 45 more 6B pencils are put in the bag, the probability of randomly picking a 6B pencil now will be quadruple that of the previous probability of picking a 6B pencil. With the given information, evaluate the original number of 6B shade in the pencil bag.An analyst is presented with lists of 4 stocks and 5 bonds. He is asked to predict, in order, the 2 stocks that will yield the highest return over the next year and the 2 bonds that will have the highest return over the next year. Suppose that these predictions are made randomly and independently of each other. What is the probability that the analyst will be successful in at least 1 of the 2 tasks?
- Give 7 other examples of random variables.Please solve it as soon as possibleA small computer lab has 2 terminals. The number of students working in this lab is recordedat the end of every hour. A computer assistant notices the following pattern:- If there are 0 or 1 students in a lab, then the number of students in 1 hour has a50-50% chance to increase by 1 or remain unchanged. - If there are 2 students in a lab, then the number of students in 1 hour has a 50-50%chance to decrease by 1 or remain unchanged. (a) Write the transition probability matrix for this Markov chain.(b) Suppose there is nobody in the lab at 7 am. What is the probability of nobody workingin the lab at 10 am?
- Suppose we have a bucket of 20 balls with 10 red and 10 green. We take 5 draws and after each draw, we remove the chosen ball from the bucket before our next draw (this is called drawing without replacement). Can we use the binomial distribution to model this scenario? Why or why not?When X is a binomial random variable, the mean of the probability distribution = np. A jury has 12 people on the jury. If a certain town has a population that is 9 percent a certain race, how many people of that race would you expect would be on the jury if jury selection was random (and every person was equally likely to be on the jury). Round answers to 4 decimal places as needed.Suppose that the population is 1000 people and the probability of cat people is 25% if we take a random sample of 100 people what is the probability that the proportion in the sample will be bigger than 29%
- can you help me do #8 and show workThe more people with COVID, the more staff you need in the ER. Let’s say approximately 5% percent of patients are coming in COVID positive. Assume that the ER will see 145 people today. Use =BINOMDIST() to determine binomial probabilities that the health department will see no one with COVID today, 1 woman with COVID, 2 women with COVID and so on, up to 21 women with COVID.This is about Binomial Distribution, need help understanding how to solve the problem