In a large population, 61% of the people have been vaccinated. If 4 people are randomly selected, what is the probability that AT LEAST ONE of them has been vaccinated? Give your answer as a decimal to 4 places. Use the following probabilities to answer the question. Round to 4 decimal places. P(A) = 0.16, P(B) = 0.79, P(A and B) = 0.05. P(B | A) = The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $9 each and will sell 800 tickets. There is one $1,000 grand prize, four $300 second prizes, and fourteen $20 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent. S 48% of all violent felons in the prison system are repeat offenders. If 41 violent felons are randomly selected, find the probability that a. Exactly 20 of them are repeat offenders. b. At most 18 of them are repeat offenders. C. At least 17 of them are repeat offenders. d. Between 16 and 21 (including 16 and 21) of them are repeat offenders. A bus comes by every 15 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 15 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the person will wait more than 4 minutes is d. Suppose that the person has already been waiting for 2.7 minutes. Find the probability that the person's total waiting time will be between 5.4 and 7.1 minutes e. 50% of all customers wait at least how long for the train? minutes. Private nonprofit four-year colleges charge, on average, $26,414 per year in tuition and fees. The standard deviation is $6,925. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 24,570 per year. c. Find the 62nd percentile for this distribution. $ (Round to the nearest dollar.) The table summarizes results from pedestrian deaths that were caused by automobile accidents. Driver Pedestrian Intoxicated? Intoxicated? Yes No Yes 64 86 No 266 568 If one of the pedestrian deaths is randomly selected, find the probability that the driver was not intoxicated. (Please enter a decimal, and round your answer to 4 decimal places.) Probability =