eAcme Company manufactures widgets. The distribution of widget weights is bell-shaped. The Iget weights have a mean of 42 ounces and a standard deviation of 5 ounces. e the Empirical Rule. ggestion: sketch the distribution in order to answer these questions. 58% of the widget weights lie between 37 of and What percentage of the widget weights lie between 27 and 47 ounces? 34 What percentage of the widget weights lie below 52 ? 0.84134 uestion Help: DVideo D Post to forum E Calculator

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### Understanding the Distribution of Widget Weights

The Acme Company manufactures widgets, and the distribution of widget weights is bell-shaped. The widget weights have a mean (average) of 42 ounces and a standard deviation of 5 ounces.

To analyze this distribution, we will employ the Empirical Rule.

#### Using the Empirical Rule

**Suggestion**: Sketch the distribution to answer these questions effectively.

1. **Determine the range for 68% of the widget weights**
   - 68% of the widget weights lie between **37** and **47** ounces.

2. **Calculate the percentage of widget weights between specific ranges**
   - **What percentage of the widget weights lie between 27 and 47 ounces?**
     - Answer: **34** %

3. **Calculate the percentage of widget weights below a certain value**
   - **What percentage of the widget weights lie below 52 ounces?**
     - Input: **0.84134** [This appears to be incorrect based on the red 'X' mark]

#### Navigation and Tools
- **Question Help**:
  - [Video](#) – Link to an explanatory video for additional assistance.
  - [Post to forum](#) – Option to ask questions or discuss with peers on a forum.
- **Calculator**: A tool to perform calculations.
- **Submit Question**: Button to submit your answers for evaluation.

---

### Visual Elements Note
- **Mean (μ)**: 42 ounces
- **Standard Deviation (σ)**: 5 ounces
- **Empirical Rule Coverage**:
  - 68% of data falls within ±1σ (37 to 47 ounces)
  - The question involves interpreting these values and understanding their implications in a normal distribution.
Transcribed Image Text:### Understanding the Distribution of Widget Weights The Acme Company manufactures widgets, and the distribution of widget weights is bell-shaped. The widget weights have a mean (average) of 42 ounces and a standard deviation of 5 ounces. To analyze this distribution, we will employ the Empirical Rule. #### Using the Empirical Rule **Suggestion**: Sketch the distribution to answer these questions effectively. 1. **Determine the range for 68% of the widget weights** - 68% of the widget weights lie between **37** and **47** ounces. 2. **Calculate the percentage of widget weights between specific ranges** - **What percentage of the widget weights lie between 27 and 47 ounces?** - Answer: **34** % 3. **Calculate the percentage of widget weights below a certain value** - **What percentage of the widget weights lie below 52 ounces?** - Input: **0.84134** [This appears to be incorrect based on the red 'X' mark] #### Navigation and Tools - **Question Help**: - [Video](#) – Link to an explanatory video for additional assistance. - [Post to forum](#) – Option to ask questions or discuss with peers on a forum. - **Calculator**: A tool to perform calculations. - **Submit Question**: Button to submit your answers for evaluation. --- ### Visual Elements Note - **Mean (μ)**: 42 ounces - **Standard Deviation (σ)**: 5 ounces - **Empirical Rule Coverage**: - 68% of data falls within ±1σ (37 to 47 ounces) - The question involves interpreting these values and understanding their implications in a normal distribution.
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