10 Suppose that the average number of Facebook friends users have is normally distributed with a mean of 129 and a standard deviation of about 46. Assume forty-eight individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. a. What is the distribution of 27 2 ~ N( b. For the group of 48, find the probability that the average number of friends is more than 132. C. Find the third quartile for the average number of Facebook friends. d. For part b), is the assumption that the distribution is normal necessary? O Yes No11 The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.3 ppm and standard deviation 1.8 ppm. 38 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 ? C ~ N( c. What is the probability that one randomly selected city's waterway will have less than 9.9 ppm pollutants? d. For the 38 cities, find the probability that the average amount of pollutants is less than 9.9 ppm. e. For part d), is the assumption that the distribution is normal necessary? O NoO Yes f. Find the IQR for the average of 38 cities. Q1 = ppm Q3 = ppm IOR: Ppmi11 V 'C 2* The amount of syrup that people put on their pancakes is normally distributed 1with mean 59 mL and standard deviation 8 mL. Suppose that 49 randomly selected people are observed pouring syrup on their pancakes. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ iii| H I} . . l] c. If a single randomly selected individual is observed, find the probability that this person consumes is between 59.? mL and 50.9 mL. | | I b. What is the distribution of it? s ~ N{| d. For the group of 49 pancake eaters, find the probability that the average amount of syrup is between 59.? mL and so}; mL.| | e. For part d}, is the assumption that the distribution is normal necessary? '3?! Moi:1 Yes [ll4.. 13