The amount of pollutants that are found in waterways near large cities is normally distributed with mean 8.5 ppm and standard deviation 1.8 ppm. 40 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N([:,[:]) b. What is the distribution of E? 5 ~ N([:],:]} c. What is the probability that one randomly selected city's waterway will have less than 9.3 ppm pollutants? d. For the 40 cities, find the probability that the average amount of pollutants is less than 9.3 ppm. S e. For part d), is the assumption that the distribution is normal necessary? 0 N00 Yes The average price of a college math textbook is $161 and the standard deviation is $28. Suppose that 7 textbooks are randomly chosen. Round all answers to 4 decimal places where possible. a. What is the distribution of :E? 5 ~ WELD} b. For the group of 7, find the probability that the average price is between $159 and $174. C] c. Find the third quartile for the average textbook price for this sample size. SS (round to the nearest cent) d. For part b), is the assumption that the distribution is normal necessary? 0 YesO No Question Help: Q Written Example 8 Message instructor Suppose that the number of Facebook friends users have is normally distributed with a mean of 143 and a standard deviation of about 42. Assume seventeen individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. a. What is the distribution of :E? :2": ~ N([:],:]} b. For the group of 17, find the probability that the average number of friends is more than 142. c. Find the first quartile for the average number of Facebook friends. Round to 2 decimal places. [:1 d. For part b), is the assumption that the distribution is normal necessary? 0 N00 Yes The lengths of adult males' hands are normally distributed with mean 185 mm and standard deviation is 7.2 mm. Suppose that 16 individuals are randomly chosen. Round all answers to 4 where possible. a. What is the distribution of :E? 5 ~ WELD} b. For the group of 16, find the probability that the average hand length is less than 183. C] c. Find the first quartile for the average adult male hand length for this sample size. Round to 2 decimal places. [3 d. For part b), is the assumption that the distribution is normal necessary? 0 YesO No Question Help: Q Written Example 8 Message instructor The average number of miles (in thousands) that a car's tire will function before needing replacement is 68 and the standard deviation is 16. Suppose that 45 randomly selected tires are tested. Round all answers to 4 decimal places where possible and assume a normal distribution. a. What is the distribution of X? X ~ N([:,[:]) b. What is the distribution of E? 5 ~ N([:],:]) c. If a randomly selected individual tire is tested, find the probability that the number of miles (in thousands) before it will need replacement is between 68.9 and 70.8. [: d. For the 45 tires tested, find the probability that the average miles (in thousands) before need of replacement is between 68.9 and 70.8. C] e. For part d), is the assumption that the distribution is normal necessary? 0 YesO No