Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 42 minutes and standard deviation 21 minutes. A researcher observed 50 students who entered the library to study. Round all answers to 4 decimal places where possible.

1. What is the distribution ofXX?XX~ N(,)
2. What is the distribution ofxx?xx~ N(,)
3. What is the distribution ofxx?xx~ N(,)
4. If one randomly selected student is timed, find the probability that this student's time will be between 40 and 41 minutes.
5. For the 50 students, find the probability that their average time studying is between 40 and 41 minutes.
6. Find the probability that the randomly selected 50 students will have a total study time more than 2250 minutes.
7. For part e) and f), is the assumption of normal necessary?YesNo
8. The top 10% of the total study time for groups of 50 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