QuestionSuppose 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 20 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 $X$ ? $X \sim N($ $\square$ $\square$ ) b. What is the distribution of $\bar{x}$ ? $\bar{x} \sim N($ $\square$ $\square$ ) c. What is the distribution of $\square$ $x$ ? $\square$ $x \sim \mathrm{~N}($ $\square$ , $\square$ ) d. If one randomly selected student is timed, find the probability that this student's time will be between 33 and 44 minutes. $\square$ e. For the 6 students, find the probability that their average time studying is between 33 and 44 minutes. $\square$ f. Find the probability that the randomly selected 6 students will have a total study time less than 312 minutes. $\square$ g. For part e) and f), is the assumption of normal necessary? Yes No h. The top $15 \%$ 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? $\square$ minutes