14. Ten percent of American adults are left-handed. A statistics class has 30 students in attendance. a) Find the mean and standard deviation for the number of left-handed students in such classes of 30 students. b) Would it be unusual to survey a class of 30 students and find that 10 of them are left-handed? Why or why not? 15. In one year (365 days), there were 116 homicide deaths in Richmond, Virginia. Find the mean number of deaths per day and find the probability that a randomly selected day has the following numbers of homicide deaths. a) 0,b) 1, c) 2, d) 3. Compare your calculated probabilities to these actual results: 268 days (0 homicides); 79 days (1 homicide); 17 days (2 homicides); 1 day (3 homicides). Does the Poisson distribution serve as a good device for predicting the actual results? 16. a) A quiz consists of 15 multiple-choice questions, each with 5 possible answers. For someone who makes random guesses for all answers, find the probability of passing if the minimum passing grade is 60%. b) Bob is a self-proclaimed mentalist" who claims that he can pass true/false tests by guessing. In a test of his claim, he is given 14 true/false questions, and he manages to correctly guess the answers to 2 of them. Is the number of correct answers unusual? Why or why not. Does Bob's claim appear to be valid? 17. The amount of time spent by a statistical consultant with a client at their first meeting is a random variable having a normal distribution with mean value 60 min and standard deviation 10 min. a) What is the probability that more than 45 minutes is spent at the first meeting? b) What amount of time is exceeded by only 10% of all clients? 18. Suppose that only 40% of all drivers in a certain region regularly wear a seat belt. A random sample of 500 drivers is selected. a) What is the probability that at least half of those in the sample regularly wear seat belts? b) What is the probability that between 125 and 250 (inclusive) of those in the sample regularly wear a seat belt? 19. A recent survey showed that among 2013 randomly selected adults, 1358 stated that they are Internet users. If the percentage of all adults using the Internet is actually 67%, find the probability that a random sample of 2013 adults will result in exactly 1358 Internet users. 20. A lecture period at a certain college lasts exactly 50 minutes. The actual lecture time of a professor on any particular day is a random variable with mean value 52 min. and standard deviation 2 min. Suppose that times of different lectures are independent of one another and a sample of 36 lecture times are randomly selected. a) What is the probability that one randomly selected lecture time exceeds 55 min? b) What is the probability that the sample mean exceeds 55 min?