Ir ent Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 44 minutes and standard deviation 18 minutes. A researcher observed 43 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 a? a; - ND,[:) c. What is the distribution of Z 3:? Z a: - N(:],:]) d. if one randomly selected student is timed, find the probability that this student's time will be between 41 and 44 minutes. :] e. For the 43 students, find the probability that their average time studying is between 41 and 44 i. Find the probability that the randomly selected 43 students will have a total study time less than 2064 minutes. g. For part e) and r). is the assumption of normal necessary? 0 YesO No h. The top 15% of the total study time for groups of 43 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? Ewes