question 11

Let X be a random variable with the following probability distribution. Value x of X P(X=x) 20 0.35 30 0.30 40 0.10 50 0.15 60 0.05 70 0.05 (a) Find the expectation E (X) of X. X E (X) = 0 5 ? (b) Find the variance Var(X) of 1. var (x) = 0Let X be a random variable with the following probability distribution. Value x of X P(X=x) -30 0.10 -20 0.15 -10 0.05 0 0.15 10 0.15 20 0.40 Complete the following. (If necessary, consult a list of formulas.) (a) Find the expectation E (X) of X. E(X) = 1 X 5 ? (b) Find the variance Var(X) of X. var (X) = 1The workers' union at a certain university is quite strong. About 96% of all workers employed by the university belong to the workers' union. Recently, the workers went on strike, and now a local TV station plans to interview a sample of 20 workers, chosen at random, to get their opinions on the strike. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of workers in the sample who are union members by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places. Not all visitors to a certain company's website are customers or potential customers. In fact, the company's executives estimate that about 5% of all visitors to the website are looking for other websites. Assume that this estimate is correct and that a random sample of 50 visitors to the website is taken. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of visitors in the sample who actually are looking for the company's website by giving the X \\(3 I) mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your ' response. [I] (b) Quantity the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places. A machine that manufactures automobile pistons is estimated to produce a defective piston 3% of the time. Suppose that this estimate is correct and that a random sample of 80 pistons produced by this machine is taken. Answer the following. (If necessary, consult a list of formulas.) (a) Estimate the number of pistons in the sample that are defective by giving the mean of the relevant distribution (that is, the expectation of the relevant random variable). Do not round your response. [I] (b) Quantify the uncertainty of your estimate by giving the standard deviation of the distribution. Round your response to at least three decimal places. Not all visitors to a certain company's website are customers. In fact, the website administrator estimates that about 12% of all visitors to the website are looking for other websites. Assuming that this estimate is correct, find the probability that, in a random sample of 4 visitors to the website, exactly 2 actually are looking for the website. Round your response to at least three decimal places. (If necessary, consult a list of formulas.) O X 5A machine that manufactures automobile parts produces defective parts 12% of the time. If 7 parts produced by this machine are randomly selected, what is the probability that fewer than 2 of the parts are defective? Cam.r your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.) x b "D From experience, an airline knows that only 70% of the passengers booked for a certain flight actually show up. If 9 passengers are randomly selected, find the probability that at most 7 of them show up. Carry your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.) X 5 ?Suppose that the New England Colonials baseball team is equally likely to win a game as not to win it. If 5 Colonials games are chosen at random, what is the probability that exactly 2 of those games are won by the Colonials? Rounc. your response to at least three decimal places. (If necessary, consult a list of formulas.) A new surgery.r is successful 70% ofthe time. If the results of 10 such surgeries are randomly:r sampled, what is the probability that at least 8 of them are successful? Cam.r your intermediate computations to at least four decimal places, and round your answer to two decimal places. (If necessary, consult a list of formulas.) [D x 53 9