1) A company's customer service hotline handles several calls a day. Their records indicate that the average length of a phone call is 4.4 minutes with a standard deviation of 1.9 minutes. The distribution of times follows a normal distribution. a) Find the z-score corresponding to a phone call length of 6.2 minutes. b) Sketch a normal curve for this distribution including labels for 13 standard deviations along with their percentages. c) What percentage of phone calls would you expect to be at least 6.3 minutes? d) What length of time would you expect 68% of the phone calls to be in between? 2) Suppose your college Statistics professor reports test grades as z-scores and you got a score of 2.20 on an exam. Interpret this score. 3) On the 2009 PGA tour, Tiger Woods had an average driving distance of 298 yards. Assuming that his distribution of driving distances follows a normal distribution with a standard deviation of 12 yards, answer the following questions. a) What proportion of his drives would you expect to be less than 270 yards? b) What proportion of his drives would you expect to be more than 280 yards? 4) Some IQ tests are standardized to a Normal distribution with a mean of 100 and a standard deviation of 16. a) In what interval would you expect the middle 99.7%% of IQ scores to be found? b) What proportion of people do you expect to have IQ scores less than 90?5) A tire manufacturer believes that the treadlife of its snow tires can be described by a normal distribution with a mean of 32,000 miles and a standard deviation of 2,500 miles. a) What proportion of tires last between 25,000 and 35,000 miles? b) Would it be reasonable for you to expect your tires to last longer than 40,000 miles? Show work to support your answer. 6) In humans, the average length of a pregnancy is 266 days. Suppose that the distribution of pregnancy lengths can be modeled by a normal distribution with a standard deviation of 10 days. a) What proportion of pregnancies will last fewer than 270 days? b) What proportion of pregnancies will last longer than 250 days? c) What proportion of women will deliver their babies between 259 and 273 days