MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![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.](https://content.bartleby.com/qna-images/question/ef4421a9-80f4-44ac-a84c-7924c290e1b7/7753f575-8fdc-48dc-9609-bd71e4469d53/vbzxc1t_processed.jpeg)
Transcribed Image Text: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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