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

Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 45 minutes and standard deviation 20 minutes. A researcher observed 48 students who entered the library to study. Round all answers to 4 decimal places where possible.

1. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)


2. If one randomly selected student is timed, find the probability that this student's time will be between 42 and 46 minutes.


3. For the 48 students, find the probability that their average time studying is between 42 and 46 minutes.