**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

Answered: Image /qna-images/answer/d6e7d316-f6da-4610-9e63-dab87ce53034.jpg

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

See similar textbooks

Similar questions

Given the normal distribution represented by X ~ N(81.8, 3.4). Find the 70th percentile to the nearest tenth. a.85.7 b.87.7 c.83.6 d.85.6
Need help with this one. Need a step by step explanation please.
Please only do that one that is incorrect Or isn't done
The avg. production…
4
The following frequency table shows the number of fires per month in a city. Complete the table entries to find the mean and standard deviation for this distribution. E Click the icon to view the table. Complete the table below. More Info (Type integers or decimals rounded to three decimal places as needed.) 21 Product, Number, Frequency, Product, Deviation, Deviation 2 2 (x-x) (x-x)²•f 21 f (x•f) (x-x)² Number, Frequency, Product, f Deviation, Deviation (x•f) (x-x) (x-x)² X-X 2 X-X 4. 3 1 6. 0. Ex-73D Print Done Help me solve this View an example Get more help - 99+
1. The amount of time a Tech student spends on Instagram has an approximately exponential distribution with mean 60 minutes. a. What is the probability a randomly selected student spends less than 45 on Instagram? b. Illustrate your answer from a. using the pdf c. Find the cumulative distribution function for the time students spend on Instagram. d. What is the probability a randomly selected student is on Instagram for a time within 2 standard deviation of the mean?
Please only answer b c d
Assume that the readings on the thermometers are normally distributed with a mean of 0 degrees and standard deviation of 1.00 degrees C. A thermometer is randomly selected and tested. Draw a sketch and find the temperature reading corresponding to Upper P 84, the 84 th percentile. This is the temperature reading separating the bottom 84 % from the top 16 %. A. Which graph represents Upper P 84? B. The temperature for Upper P 84 is approximately (Round to two decimal places as needed.)
Help with c and d
Recall the histogram of annual maximum wind speed. Frequency оооооо 25 to 30 30 to <35 35 to 40 A histogram with a single peak is unimodal. A histogram with two peaks is bimodal. A histogram with more than two peaks is multimodal. Look over the histogram again and notice the number of peaks, or modes, in the distribution. Indicate below the class interval(s) where a peak occurs. (Select all that apply.) 40 to 45 45 to < 50 50 to < 55 55 to < 60 14 12 10 60 to < 65 co 4 25 30 35 40 45 50 55 60 65 annual maximum wind speed
Help with c ,d and f