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 17 minutes. A researcher observed 6...

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 17 minutes. A researcher observed 6 students who entered the library to study. Round all answers to 4 decimal places where possible.

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4. If one randomly selected student is timed, find the probability that this student's time will be between 48 and 56 minutes.


5. For the 6 students, find the probability that their average time studying is between 48 and 56 minutes.


6. Find the probability that the randomly selected 6 students will have a total study time less than 258 minutes.


7. For part e) and f), is the assumption of normal necessary?NoYes


8. 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?minutes