Lunch break: In a recent survey of 608 working Americans ages 25-34, the average weekly amount spent on lunch as $45.08 with standard deviation $2.66. The weekly amounts are approximately bell-shaped. Part: 0 / 3 Part 1 of 3 (a) Estimate the percentage of amounts that were less than $42.42. Round the answer to one decimal place. Approximately % of the amounts were less than $42.42.
Lunch break: In a recent survey of 608 working Americans ages 25-34, the average weekly amount spent on lunch as $45.08 with standard deviation $2.66. The weekly amounts are approximately bell-shaped. Part: 0 / 3 Part 1 of 3 (a) Estimate the percentage of amounts that were less than $42.42. Round the answer to one decimal place. Approximately % of the amounts were less than $42.42.
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
![**Lunch break:** In a recent survey of 608 working Americans ages 25-34, the average weekly amount spent on lunch is $45.08 with a standard deviation of $2.66. The weekly amounts are approximately bell-shaped.
### Part: 0 / 3
### Part 1 of 3
(a) Estimate the percentage of amounts that were less than $42.42. Round the answer to one decimal place.
Approximately ______ % of the amounts were less than $42.42.
(There is a text box and buttons for submitting the response, resetting the input, and cancelling the input. The buttons have the symbols 'X', '⟲', and a check mark respectively).
---
**Explanation for Educators:**
This exercise involves understanding the concepts of mean, standard deviation, and the bell-shaped (normal) distribution. Using the given parameters, students are expected to calculate the percentage of amounts below a certain value using the properties of the normal distribution.
1. **Mean ($\mu$):** The average weekly amount spent on lunch is $45.08.
2. **Standard Deviation ($\sigma$):** The standard deviation is $2.66.
3. **Value to Compare ($X$):** The amount to be compared is $42.42.
Since the distribution is approximately normal, students can use the Z-score formula to find the required percentage:
\[ \text{Z} = \frac{X - \mu}{\sigma} \]
1. Compute the Z-score.
2. Use the Z-score table to find the corresponding percentage of values below this Z-score.
3. Round the result to one decimal place as instructed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8f283cfc-3082-4072-ac5d-2906bb7d4620%2F49399588-cb32-4341-96d8-e919999c4a71%2Fdbuuvrp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Lunch break:** In a recent survey of 608 working Americans ages 25-34, the average weekly amount spent on lunch is $45.08 with a standard deviation of $2.66. The weekly amounts are approximately bell-shaped.
### Part: 0 / 3
### Part 1 of 3
(a) Estimate the percentage of amounts that were less than $42.42. Round the answer to one decimal place.
Approximately ______ % of the amounts were less than $42.42.
(There is a text box and buttons for submitting the response, resetting the input, and cancelling the input. The buttons have the symbols 'X', '⟲', and a check mark respectively).
---
**Explanation for Educators:**
This exercise involves understanding the concepts of mean, standard deviation, and the bell-shaped (normal) distribution. Using the given parameters, students are expected to calculate the percentage of amounts below a certain value using the properties of the normal distribution.
1. **Mean ($\mu$):** The average weekly amount spent on lunch is $45.08.
2. **Standard Deviation ($\sigma$):** The standard deviation is $2.66.
3. **Value to Compare ($X$):** The amount to be compared is $42.42.
Since the distribution is approximately normal, students can use the Z-score formula to find the required percentage:
\[ \text{Z} = \frac{X - \mu}{\sigma} \]
1. Compute the Z-score.
2. Use the Z-score table to find the corresponding percentage of values below this Z-score.
3. Round the result to one decimal place as instructed.
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Follow-up Questions
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Follow-up Question
![### Lunch Break Spending Statistics
---
**Context:** In a recent survey of 608 working Americans ages 25-34, the average weekly amount spent on lunch was $45.08 with a standard deviation of $2.66. The weekly amounts are approximately bell-shaped.
---
#### Part 1 of 3
**Question:** Estimate the percentage of amounts that were less than $42.42. Round the answer to one decimal place.
**Answer:** Approximately **16%** of the amounts were less than $42.42.
**Completion Indicator:** The progress bar for this question shows 1/3 is complete.
---
#### Part 2 of 3
**Question:** Estimate the percentage of amounts that were greater than $50.40. Round the answer to one decimal place.
**Answer:** The percentage is to be determined and entered in the provided input box.
**Interactive Elements:**
- A progress bar indicating the current position within the multipart question.
- A submit/reset button for answering the question.
---
### Descriptions of Visual Elements
- **Progress Bar:** Indicates the completion status of the multipart question.
- **Check Mark Icon:** Indicates that the answer provided in Part 1 is correct.
- **Input Fields:** Areas where participants can enter their estimated percentages.
- **Buttons:**
- **Submit:** For submitting the answer.
- **Reset:** For clearing the response to re-enter a new answer.
---](https://content.bartleby.com/qna-images/question/8f283cfc-3082-4072-ac5d-2906bb7d4620/d64b79d4-4541-4aae-89f2-d1bc740ea6ad/nggmqi_thumbnail.jpeg)
Transcribed Image Text:### Lunch Break Spending Statistics
---
**Context:** In a recent survey of 608 working Americans ages 25-34, the average weekly amount spent on lunch was $45.08 with a standard deviation of $2.66. The weekly amounts are approximately bell-shaped.
---
#### Part 1 of 3
**Question:** Estimate the percentage of amounts that were less than $42.42. Round the answer to one decimal place.
**Answer:** Approximately **16%** of the amounts were less than $42.42.
**Completion Indicator:** The progress bar for this question shows 1/3 is complete.
---
#### Part 2 of 3
**Question:** Estimate the percentage of amounts that were greater than $50.40. Round the answer to one decimal place.
**Answer:** The percentage is to be determined and entered in the provided input box.
**Interactive Elements:**
- A progress bar indicating the current position within the multipart question.
- A submit/reset button for answering the question.
---
### Descriptions of Visual Elements
- **Progress Bar:** Indicates the completion status of the multipart question.
- **Check Mark Icon:** Indicates that the answer provided in Part 1 is correct.
- **Input Fields:** Areas where participants can enter their estimated percentages.
- **Buttons:**
- **Submit:** For submitting the answer.
- **Reset:** For clearing the response to re-enter a new answer.
---
Solution
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