. Question 6 v The lengths of adult males' hands are normally distributed with mean 188 mm and standard deviation is ?'.1 mm. Suppose that 41 individuals are randomly chosen. Round all answers to 4 where possible. a. What is the distribution of 5'? f v N{:],:|} b. For the group of 41, find the probability that the average hand length is more than 18?. :l E. Find the first quartile for the average adult male hand length for this sample size. |:| d. For part b}, is the assumption that the distribution is normal necessary? 0 'r'esC' No . Question ? 1' The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.3 ppm and standard deviation 1.3 ppm. 13 randomly selected large cities are studied. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X ~ N|{|:],|:]] c. What is the probability that one randomly selected city's waterway will have more than 1.2 ppm d. For the 13 cities, find the probability that the average amount of pollutants is more than 1'02 ppm. :l e. For part d}, is the assumption that the distribution is normal necessary? 0 NoCI Yes f. Find the IQR for the average of 13 cities. ppm ppm ppm . Question 3 'r Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 49 minutes and standard deviation 20 minutes. A researcher observed 13 students who entered the library to study. Round all answers to 4 decimal places where possible. :I'I'J'a . What is the dim-bum\" of x? x H{|:|,:|, . What is the distribution of E? {E v HE'S} . What is the distribution of Z 2.? 2: ~ \"(Ciil . If one randomly selected student is timed, find the probability that this student's time will be between 45 and 51 minutes. :] . For the 13 students, find the probability that their average time studying is between 45 and 51 . Find the probability that the randomly selected 18 students will have a total study time more than 936 minutes. . For part e]: and f], is the assumption of normal necessary? O \"00 Yes . The top 15% of the total study time for groups of 18 students will be given a sticker that says "Great dedication". What is the least total time that a group can study and still receive a sticker