Question D and H are the only wrong answers

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 21 minutes. A researcher observed 44 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( 46 21 b. What is the distribution of ? ~ ~ N( 46 3.1659 c. What is the distribution of > a? a ~ N( 2024 139.2982 d. If one randomly selected student is timed, find the probability that this student's time will be between 48 and 51 minutes. 0.0550 X e. For the 44 students, find the probability that their average time studying is between 48 and 51 minutes. 0.2072 f. Find the probability that the randomly selected 44 students will have a total study time more than 2112 minutes. 0.2643 g. For part e) and f), is the assumption of normal necessary? O Yes No h. The top 15% of the total study time for groups of 44 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? 2168.3129 minutes