The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 43 ounces and a standard deviation of 6 ounces.

Use the Empirical Rule.

Suggestion: sketch the distribution in order to answer these questions.

a) 99.7% of the widget weights lie between 
 and

The Empirical Rule states that for a normal distribution:

- **68%** of data falls within **1 standard deviation** of the mean.
- **95%** of data falls within **2 standard deviations** of the mean.
- **99.7%** of data falls within **3 standard deviations** of the mean.

Given that the mean is \(43\) ounces and the standard deviation is \(6\) ounces:

### To find the range where 99.7% of the weights lie:
We need to calculate 3 standard deviations above and below the mean:

- **Lower Bound**: \( 43 - 3 \times 6 = 43 - 18 = 25 \) ounces
- **Upper Bound**: \( 43 + 3 \times 6 = 43 + 18 = 61 \) ounces

### Answer:
99.7% of the widget weights lie between **25 ounces** and **61 ounces**.

Would you like a detailed explanation on how this applies to real-world data analysis or any other questions on this topic?

Here are 5 related questions to further explore this topic:
1. What range would contain 95% of the widget weights?
2. How would you determine the percentage of widgets that weigh more than 49 ounces?
3. What is the probability of a widget weighing between 37 and 49 ounces?
4. How does the Empirical Rule relate to the concept of z-scores?
5. How would outliers affect the distribution in a real-world scenario?

**Tip**: The Empirical Rule is only applicable to distributions that are approximately normal (bell-shaped).

The Acme Company manufactures widgets. The distribution of widget weights is bell-shaped. The widget weights have a mean of 43 ounces and a standard deviation of 6 ounces. Use the Empirical Rule. a) 99.7% of the widget weights lie between ______ and ______.

Learn how to apply the Empirical Rule to determine the range where 99.7% of widget weights lie, given a normal distribution with a mean of 43 ounces and a standard deviation of 6 ounces. Understand key statistical concepts like standard deviation and normal distribution in this detailed explanation. Suitable for high school students in Grades 10-12.

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