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6. Of the members of a particular Poker club, 60% play Hold 'em regularly, 55% play Seven Card Stud regularly. and 30% play both Hold 'em and Seven Card Stud regularly. a) If members are selected at random, what is the probability that he or she will play either Hold 'em or Seven Card Stud regularly? b) Are the events "plays Hold 'em regularly" and "plays Seven Card Stud regularly" independent? Explain. c) Are the events "plays Hold 'em regularly" and "plays Seven Card Stud regularly" mutually exclusive? Explain. 7. Suppose that 20% of professional comedians quit performing by the time they are 40 years of age. a) If 15 professional comedians are selected at random, what is the probability that at least 5 will quit by age 40? b) If 16 professional comedians are selected at random, what is the probability that exactly 2 will quit by age 40? 8. Find the expected value and variance of the probability distribution at 2 3 the right. PX) 0.2 0.3 0.3 0.1 0.1 9. Scores from a statistics exam are normally distributed with a mean of 78 and a standard deviation of 6. a) What is the probability that a randomly selected student (who took that particular exam) will score above an 88? b) How high a score would a person need to be in the top 15% on this particular exam? 10. In a random sample of 200 Mizzou football fans, 160 said they were already excited about next year's season of Tiger football. a) Find a 95% Confidence Interval for the true proportion of Mizzou football fans that are excited about the upcoming football season. b) To estimate the true proportion of Mizzou fans that are excited about the upcoming football season to within 0.04 with 95% confidence, what sample size is needed