Please show all work written out on paper (please not through excel):
1) A survey of students found that 86% expect to pass the statistics test they are scheduled to take next week. If twelve students are interviewed, what is probability that exactly eight will expect to pass next week's test?
2) Historical data shows that customers arrive at the drive-thru window of a credit union at the rate of five cars every ten minutes on weekday mornings. Assuming the rate is consistent and the cars arrive independently, what is the chance that exactly eight cars will arrive between the hours of 10:00am and 10:30am next Friday morning?
3) According to a recent survey, 35% of respondents own a gun. From a random sample of eighteen respondents, what is the probability that the number owning a gun is: (a) no more than seven; (b) between eight and twelve, inclusive; (c) less than eight; (d) more than three; (e) at least sixteen?
4) After being nominated for an MTV Music Award, the probability of winning is 25%. If Taylor Swift has been nominated for five awards, what is the chance that she will win at least one? How many awards should she expect to win? What is the standard deviation associated with this probability? What's the probability that Kanye West will show up and make an ass of himself at the awards program?
5) A certain production process has an average defect rate of 1.8 defects per production cycle. Since the company loses money when excessive defects occur, the plant manager is concerned about defects reaching four or more per cycle. What is the probability that the company will experience four or more defects per cycle?
6) In the survey from problem number 5 above, it was found that 5% of people owned assault rifles. If three people are interviewed, what is the probability that none of them own an assault rifle? Use a tree diagram (decision/contingency tree) to work this problem.