Question

# Suppose that the amount of time that students spend studying in the library in one sitting...

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 21 minutes. A researcher observed 46 students who entered the library to study. Round all answers to 4 decimal places where possible.

1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the distribution of ∑x∑x? ∑x∑x ~ N(,)
4. If one randomly selected student is timed, find the probability that this student's time will be between 42 and 47 minutes.
5. For the 46 students, find the probability that their average time studying is between 42 and 47 minutes.
6. Find the probability that the randomly selected 46 students will have a total study time less than 1932 minutes.
7. For part e) and f), is the assumption of normal necessary? NoYes
8. The top 10% of the total study time for groups of 46 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