Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 43 minutes and standard deviation 20 minutes. A researcher observed 16...

Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 43 minutes and standard deviation 20 minutes. A researcher observed 16 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 45 and 48 minutes.


2. For the 16 students, find the probability that their average time studying is between 45 and 48 minutes.


3. Find the probability that the randomly selected 16 students will have a total study time more than 784 minutes.