Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 22 minutes. A researcher observed 6 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( b. What is the distribution of x? x - N( c. What is the distribution of a? x - N d. If one randomly selected student is timed, find the probability that this student's time will be between 38 and 46 minutes. e. For the 6 students, find the probability that their average time studying is between 38 and 46 minutes. f. Find the probability that the randomly selected 6 students will have a total study time less than 318 minutes. g. For part e) and f), is the assumption of normal necessary? O Yes No h. The top 20% of the total study time for groups of 6 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? minutes