Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 41 minutes and standard deviation 19 minutes. A researcher observed 17 students who entered the library to study. Round all answers to 4 decimal places where possible.

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If one randomly selected student is timed, find the probability that this student's time will be between 37 and 43 minutes.
For the 17 students, find the probability that their average time studying is between 37 and 43 minutes.
Find the probability that the randomly selected 17 students will have a total study time less than 731 minutes.
For part e) and f), is the assumption of normal necessary? YesNo
The top 15% of the total study time for groups of 17 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