Solve and explain for me
28. Which of the following statements is true for a continuous random variable X? a. P(X = c) = 0 for any constant c c. the total area under the curve equals one b. P(X - c) - 0 only for c = 0 a. All trials must be identical and independent d. Both (a) and (c) 29. Which of the following is NOT an assumption of the binomial experiment? b. Each trial outcomes must be classified as a success or a failure. c." The probability of success is equal to 0.5 in all trials d. The number of successes in the trials is counted. 30. The probability that a certain machine will produce a defective item is 0.20. If a random sample of 6 items is taken, what is the probability that there will be 5 or more defectives in the sample? a. 0.0016 b. 0.0154 c. 0.2458 d. 0.0001 Consider the following situation to answer questions 31-32 According to a survey, 75% of all customers will return to the same grocery store. Suppose eight customers are selected at random, a. 0.0467 31. what is the probability that exactly five of the customers will return? b. 0.2076 c. .2541 d. 0.1468 a. 8 32. How many customers would be expected to return to the same store? b: 5 C. 6 d. 7 34. The distribution of the number of people logging into a large computer network during a five second period is a. binomial b. Hypergeometric c. Poisson d. None of the above 35. A large proportion of small businesses fail during the first few years of operation. On average, 1.3 businesses fail per day in a large city. What is the probability that 3 businesses will fail on a given day in this city? a. 0.0998 b. 0.2330 c. 0.1098 d. 0.3110 36. Suppose a professor randomly selects three new teaching assistants from a total of 10 applicants, six male and four female students. The probability that no females are hired is a. 0.2500 b. 0.333 c. 0.200 d. 0.1667 37. The business department at a university has 18 faculty members. Of them, 1 1 are in favor of the proposition that all MBA students should take a course in ethics and 7 are against this proposition. If 5 faculty members are randomly selected from 18, what is the probability that the number of faculty members in this sample who are in favor of the proposition is exactly two? a. 0.2247 b. 0.2696 c. 0.0539 d. 0.3315 38. The number of customers entering a bank per minute is a Poisson random variable with a mean of 3.5 customers per minute. What is the probability that more than three customers enter the bank in a minute? d. 0.6791 a. 0.3209 b. 0.4633 c. 0.5367 39. The marketing manager of a company usually receives 10 complaint calls during a week (consisting of five working days). Suppose that the number of calls during a week follows the Poisson distribution. The probability that she gets five such calls in one day is: d. 0.2000 0.0361 b. 0.0378 c. 0.9834
