**Educational Website Transcription**---**Title:** Understanding the Distribution of Study Times in the LibrarySuppose that the amount of time that students spend studying in the library in one sitting is normally distributed with a mean of 43 minutes and a standard deviation of 20 minutes. A researcher observed 49 students who entered the library to study. Round all answers to 4 decimal places where possible.**Questions:****a. What is the distribution of $ X $?**\[ X \sim N(43, 20) \]**b. What is the distribution of $ \bar{x} $?**\[ \bar{x} \sim N\left(43, \frac{20}{\sqrt{49}}\right) = N(43, 2.8571) \]**c. What is the distribution of $ \sum x $?**\[ \sum x \sim N(43 \times 49, 20 \times \sqrt{49}) = N(2107, 140) \]**d. If one randomly selected student is timed, find the probability that this student's time will be between 44 and 47 minutes.**\[ P(44 \leq X \leq 47) = 0.0593 \]**e. For the 49 students, find the probability that their average time studying is between 44 and 47 minutes.**\[ P(44 \leq \bar{x} \leq 47) = 0.2824 \]**f. Find the probability that the randomly selected 49 students will have a total study time more than 2156 minutes.**\[ P\left(\sum x > 2156\right) = 0.3632 \]**g. For part (e) and (f), is the assumption of normal necessary?**\[ \text{Yes} \]**h. The top 20% of the total study time for groups of 49 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?**\[ \text{Answer: } \boxed{\text{minutes}} \]---This section aims to summarize statistical methods for analyzing normally distributed data, particularly focusing on student study times in the library. Here, the

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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 43 minutes and standard deviation 20 minutes. A researcher observed 49 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 43 20 b. What is the distribution of x? ¤ - N( 43 2.8571 v) o c. What is the distribution of æ? x - N( 2107 d. If one randomly selected student is timed, find the probability that this student's time will be 140 between 44 and 47 minutes. .0593 e. For the 49 students, find the probability that their average time studying is between 44 and 47 minutes. .2824 f. Find the probability that the randomly selected 49 students will have a total study time more than 2156 minutes. .3632 g. For part e) and f), is the assumption of normal necessary? NoO Yes o h. The top 20% of the total study time for groups of 49 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

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 20 minutes. A researcher observed 49 students who entered the library to study. Round all answers to 4 decimal places where possible. a. What is the distribution of X? X - N( 43 20 b. What is the distribution of x? ¤ - N( 43 2.8571 v) o c. What is the distribution of æ? x - N( 2107 d. If one randomly selected student is timed, find the probability that this student's time will be 140 between 44 and 47 minutes. .0593 e. For the 49 students, find the probability that their average time studying is between 44 and 47 minutes. .2824 f. Find the probability that the randomly selected 49 students will have a total study time more than 2156 minutes. .3632 g. For part e) and f), is the assumption of normal necessary? NoO Yes o h. The top 20% of the total study time for groups of 49 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

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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