Chapter 7: Central Limit Theorem (Sums) 0/5 13 Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 46 minutes and standard deviation 22 minutes. A researcher observed 7 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 D? C - N( C. What is the distribution of ) :? ) a - Nd d. If one randomly selected student is timed, find the probability that this student's time will be between 39 and 43 minutes. e. For the 7 students, find the probability that their average time studying is between 39 and 43 minutes. f. Find the probability that the randomly selected 7 students will have a total study time more than 259 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 7 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