. The table below depicts a probability distribution for the random variable x. x 3 6 9 p(x) .25 .50 .25 a. Compute the expected value [p or E(x)) of x. b. Compute the standard deviation (0') of x. . Suppose a random variable x follows a binomial distribution with n = 20 and p = .70. a. Calculate P[x = 12) b. Calculate P[x = 16) c. Calculate P[x 3 1) (1. Compute E[x) e. Compute 02 [Var (x)) . In San Francisco, 30% of workers take public transportation daily [ USA Today]. a. In a sample of 10 workers, what is the probability that exactly three workers take public transportation daily? b. In a sample of 10 workers, what is the probability that at least three workers take public transportation daily? . A shipment of 20 HD television sets is received by a retailer. To protect herself against a bad shipment, she will inspect 5 sets and accept the entire lot if she observes either 0 or 1 defective. Suppose that there are actually 7 defective sets in the shipment. What is the probability that she accepts the entire shipment? [In other words, what is the probability of no more than 1 defective?) . According to the National Highway Traffic Safety Administration, "As many as 9 out of 10 heavily used cars, such as those from leasing companies, may have had their mileage rolled back when resold.\" [Reported in Orlando Sentinel.) Suppose you purchase for your rm 10 used cars from an auto leasing company that has 25 cars available. Unknown to you, 60% (that is, 15) of the 25 cars have falsied odometer readings. a. What is the probability that 6 of the 10 cars you purchased have falsied odometer readings. Use the hypergeometric distribution (or combinations counting technique) here. b. Now calculate the probability asked for in [a] using the binomial distribution. Which answer - (a) or [b] - is correct? Why? 1