Question

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 19 minutes. A researcher observed 9 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 47 and 50 minutes.
5. For the 9 students, find the probability that their average time studying is between 47 and 50 minutes.
6. Find the probability that the randomly selected 9 students will have a total study time more than 360 minutes.
7. For part e) and f), is the assumption of normal necessary? YesNo
8. The top 15% of the total study time for groups of 9 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