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).