Please solve and show all work. So I can learn how to solve these equations.

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 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 I? I - N( Proctor C. What is the distribution of z? x - N d. If one randomly selected student is timed, find the probability that this student's time will be between 39 and 42 minutes. e. For the 7 students, find the probability that their average time studying is between 39 and 42 on minutes. f. Find the probability that the randomly selected 7 students will have a total study time more than 371 minutes. g. For part e) and f), is the assumption of normal necessary? O Yes No ebook h. The top 15% 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 Forms