The image contains a problem related to the distribution of study times for students in a library setting. Here's a transcription suitable for an educational website:---**Problem Context:**Suppose that the amount of time students spend studying in the library in one sitting is normally distributed with a mean of 40 minutes and a standard deviation of 19 minutes. A researcher observed 13 students who entered the library to study. Round all answers to 4 decimal places where possible.**Questions:**a. What is the distribution of $ X $? $ X \sim N(40, 19) $ b. What is the distribution of $ \bar{x} $? $ \bar{x} \sim N(40, 5.2697) $ c. What is the distribution of $ \sum x $? $ \sum x \sim N(520, 68.7805) $ *(Note: the text box contains $\times$) d. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 45 minutes. [Enter answer in textbox]e. For the 13 students, find the probability that their average time studying is between 41 and 45 minutes. [Enter answer in textbox]f. Find the probability that the randomly selected 13 students will have a total study time more than 507 minutes. [Enter answer in textbox]g. For parts (e) and (f), is the assumption of normal necessary? Options: Yes [✓] No [ ]h. The top 20% of the total study time for groups of 13 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? [Enter answer in textbox] minutes**Hint:**Some Helpful Videos:- [Link to video resources would be included on an actual webpage]---This transcription lays out the problems and the corresponding distribution notations required to solve statistical questions about the given scenario.

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Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 40 minutes and standard deviation 19 minutes. A researcher observed 13 studer who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( 40 19 b. What is thę distribution of a? a N( 40 5.2697 c. What is the distribution of x? a - N( 520 247 X) o d. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 45 minutes. e. For the 13 students, find the probability that their average time studying is between 41 and 45

Suppose that the amount of time that students spend studying in the library in one sitting is normally distributed with mean 40 minutes and standard deviation 19 minutes. A researcher observed 13 studer who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X N( 40 19 b. What is thę distribution of a? a N( 40 5.2697 c. What is the distribution of x? a - N( 520 247 X) o d. If one randomly selected student is timed, find the probability that this student's time will be between 41 and 45 minutes. e. For the 13 students, find the probability that their average time studying is between 41 and 45

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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