An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements is true, mark the appropriate box. Last year fewer than half of their dlients made a profit of 10% or less. Two years ago some of their dients made a profit of at least 10%. Last year at least one of their dlients made a profit of 10% or more. Last year at least one of their dlients made a profit of exactly 10%. O Last year all of their clients made a profit of more than 5%. O None of the above statements are true.
An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that average refers to the mean, which of the following claims must be true based on this information? Note: More than one statement could be true. If none of the statements is true, mark the appropriate box. Last year fewer than half of their dlients made a profit of 10% or less. Two years ago some of their dients made a profit of at least 10%. Last year at least one of their dlients made a profit of 10% or more. Last year at least one of their dlients made a profit of exactly 10%. O Last year all of their clients made a profit of more than 5%. O None of the above statements are true.
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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![**Question Analysis Example for Educational Website**
**Scenario:**
An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that "average" refers to the mean, consider which of the following claims must be true based on this information.
**Note:** More than one statement could be true. If none of the statements is true, mark the appropriate box.
**Statements to Evaluate:**
1. Last year fewer than half of their clients made a profit of 10% or less.
2. Two years ago some of their clients made a profit of at least 10%.
3. Last year at least one of their clients made a profit of 10% or more.
4. Last year at least one of their clients made a profit of exactly 10%.
5. Last year all of their clients made a profit of more than 5%.
6. None of the above statements are true.
To analyze the validity of each statement based on the information provided:
1. **Last year fewer than half of their clients made a profit of 10% or less.**
- This statement is checking whether the average necessarily indicates the distribution of profits among the clients.
2. **Two years ago some of their clients made a profit of at least 10%.**
- This statement refers to a period that's not covered by the average mentioned and will need additional context from other data sources to validate.
3. **Last year at least one of their clients made a profit of 10% or more.**
- To have an average of 10%, it is implied that there would be various profit levels among clients, implying that some clients must have made around or above 10%.
4. **Last year at least one of their clients made a profit of exactly 10%.**
- This statement implies that there is a specific data point exactly at 10%, which is not a necessity for calculating a mean of 10%.
5. **Last year all of their clients made a profit of more than 5%.**
- For an average (mean) to be 10%, it doesn't necessarily follow that all values must be substantially higher than a lower limit (such as 5%).
6. **None of the above statements are true.**
- This option should be considered if it's determined that none of the other statements hold given the mean profit data presented.
**Diagram/Graphs Clarification:**
- There are no](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8441b9ff-a8cf-4673-aa83-a1fcebb34e98%2F9bf7010e-8a44-4d19-a859-c287a78e5fb1%2Fkkwb6qe_processed.png&w=3840&q=75)
Transcribed Image Text:**Question Analysis Example for Educational Website**
**Scenario:**
An investment company advertised that last year its clients, on average, made a profit of 10%. Assuming that "average" refers to the mean, consider which of the following claims must be true based on this information.
**Note:** More than one statement could be true. If none of the statements is true, mark the appropriate box.
**Statements to Evaluate:**
1. Last year fewer than half of their clients made a profit of 10% or less.
2. Two years ago some of their clients made a profit of at least 10%.
3. Last year at least one of their clients made a profit of 10% or more.
4. Last year at least one of their clients made a profit of exactly 10%.
5. Last year all of their clients made a profit of more than 5%.
6. None of the above statements are true.
To analyze the validity of each statement based on the information provided:
1. **Last year fewer than half of their clients made a profit of 10% or less.**
- This statement is checking whether the average necessarily indicates the distribution of profits among the clients.
2. **Two years ago some of their clients made a profit of at least 10%.**
- This statement refers to a period that's not covered by the average mentioned and will need additional context from other data sources to validate.
3. **Last year at least one of their clients made a profit of 10% or more.**
- To have an average of 10%, it is implied that there would be various profit levels among clients, implying that some clients must have made around or above 10%.
4. **Last year at least one of their clients made a profit of exactly 10%.**
- This statement implies that there is a specific data point exactly at 10%, which is not a necessity for calculating a mean of 10%.
5. **Last year all of their clients made a profit of more than 5%.**
- For an average (mean) to be 10%, it doesn't necessarily follow that all values must be substantially higher than a lower limit (such as 5%).
6. **None of the above statements are true.**
- This option should be considered if it's determined that none of the other statements hold given the mean profit data presented.
**Diagram/Graphs Clarification:**
- There are no
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Follow-up Question
![A weight-loss clinic advertised that last month its patients, on average, lost 6 lb. Assuming that average refers to the mean, which of the following claims must
be true based on this information?
Note: More than one statement could be true. If none of the statements are true, mark the appropriate box.
This month at least one of their patients will lose at least
6 lb.
Last month all of their patients lost more than 3 lb.
Last month some of their patients lost exactly 6 lb.
Last month fewer than half of their patients lost 6 lb or
less.
Last month at least one of their patients lost at least 6 lb.
None of the above statements are true.
X
Ś](https://content.bartleby.com/qna-images/question/4373ae07-dbc5-4cb9-a237-86ce6993d370/9e5e5239-38ac-4197-98a0-881c90c81894/qjvb6s_thumbnail.png)
Transcribed Image Text:A weight-loss clinic advertised that last month its patients, on average, lost 6 lb. Assuming that average refers to the mean, which of the following claims must
be true based on this information?
Note: More than one statement could be true. If none of the statements are true, mark the appropriate box.
This month at least one of their patients will lose at least
6 lb.
Last month all of their patients lost more than 3 lb.
Last month some of their patients lost exactly 6 lb.
Last month fewer than half of their patients lost 6 lb or
less.
Last month at least one of their patients lost at least 6 lb.
None of the above statements are true.
X
Ś
Solution
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