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.

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**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.
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 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.

---
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. ---
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