1. As reported in Runner’s World magazine, the times of the finishers in the New York City 10K Run are normally distributed with a mean of 61.2 minutes and a standard deviation of 9.3 minutes. a. A runner is selected at random. Find the probability that the runner’s finishing time was more than 75 minutes. b. A runner is selected at random. Find the probability that the runner’s finishing time was between 60 and 63 minutes c. Runners whose finishing times are in the top 5% are automatically invited to participate in next year’s race. What finishing time separates the top 5% from the others? Round answer to 1 decimal place. 2. The AC Neilsen Company reports that the mean weekly television viewing time for children aged 2 – 11 years is 24.5 hours, with a standard deviation of 6.23 hours. The times are normally distributed. a. Find the percentage of children aged 2 – 11 who watch less than 20 hours of TV a week. b. What is the viewing time that separates the bottom 20% of the children from the others? c. What is the viewing time that separates the top 15% of the children from the others? 3. Cans of regular Coke are labeled as containing 12.00 oz. Assume that the actual contents are normally distributed with a mean of 12.19 oz and a standard deviation of 0.11 oz. a. What percentage of cans contain less than 12.10 oz ? b. What amount of Coke separates the top 10% of the cans from the others? c. To save some of the Coke in cans that are filled too much, the quality-control manager is instituting a plan to remove some of the Coke from cans that are in the top 2%. What is the minimum amount of Coke in such cans that will be “reworked”? d. What is the maximum amount of Coke in the cans that are in the bottom 15% ? 4. The height of an adult male is normally distributed with a mean of 69.0 inches and a standard deviation of 2.5 inches. How high should a doorway be so that 96% of the adult males can pass through it without having to bend?