. Question 3 v l | Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 42 minutes and standard deviation 16 minutes. A researcher observed 48 students who entered the library to study. Round all answers to 4 decimal places where possible. :l'l'l Hint.- . What is the distribution of X? X ~ N(:],:]} . What is the distribution of 5:? i ~ ND,:]} . What is the distribution of Z 2:? Z :1: - \"Cl'Cil . If one randomly selected student is timed, find the probability that this student's time will be between 40 and 42 minutes. C] . For the 48 students, find the probability that their average time studying is between 40 and 42 . Find the probability that the randomly selected 48 students will have a total study time more than 2112 minutes. . For part e) and f), is the assumption of normal necessary? 0 N00 Yes . The top 10% of the total study time for groups of 48 students will be given a sticker that says "G reat dedication". What is the least total time that a group can study and still receive a sticker? Bapt501399 G)