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 45...

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 45 students who entered the library to study. Round all answers to 4 decimal places where possible.

1. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 46 minutes.


2. For the 45 students, find the probability that their average time studying is between 41 and 46 minutes.


3. Find the probability that the randomly selected 45 students will have a total study time more than 1710 minutes.