Question

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 23 minutes. A researcher observed 11 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 46 and 50 minutes.
5. For the 11 students, find the probability that their average time studying is between 46 and 50 minutes.
6. Find the probability that the randomly selected 11 students will have a total study time more than 451 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 11 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

Answer 1