https://file.aiquickdraw.com/mathbot/file/1727112134767av3ky5un.jpg

Let's address each part of the question shown in the image step by step:

### Part (b):
The question asks for the appropriateness of using the Empirical Rule based on the histogram of M&M weights. The Empirical Rule (also known as the 68-95-99.7 rule) is applicable for approximately bell-shaped, symmetric distributions.

- Since the histogram appears approximately bell-shaped, the **correct answer is (A)**:  
  "The histogram is approximately bell-shaped, so the Empirical Rule can be used."

### Part (c):
To calculate the percentage of M&Ms with weights between 0.802 grams and 0.946 grams using the Empirical Rule:
- The Empirical Rule states that **95% of the data** falls within **two standard deviations** of the mean for a normal distribution.
- The provided mean is \( \bar{x} = 0.874 \) grams.
- Without standard deviation, the assumption here is that the range of 0.802 grams to 0.946 grams captures roughly two standard deviations, meaning this range represents **95%** of the data.

Thus, the answer for part (c) is **95%**.

### Part (d):
For part (d), to determine the actual percentage of M&Ms in the weight range 0.802 grams to 0.946 grams:
- This step requires access to the actual data or more detailed statistical information (e.g., standard deviation or cumulative frequency). Without this, I can’t compute the precise percentage for this part.

If you have access to raw data or additional statistics (like standard deviation), I can guide you through calculating the exact percentage. Let me know if you'd like help with that.

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Do you want further details or have any questions on these parts?

Here are 5 questions for further exploration:
1. How is the Empirical Rule useful in making predictions about data?
2. What are the conditions under which the Empirical Rule might not apply?
3. Can you identify how many standard deviations from the mean the range 0.802 to 0.946 grams represents?
4. How would you calculate the percentage if the distribution were not bell-shaped?
5. What is the significance of the 68-95-99.7 percentages in statistics?

**Tip:** When interpreting histograms, always check for symmetry and bell shape to apply the Empirical Rule effectively.

On the basis of the accompanying histogram, comment on the appropriateness of using the Empirical Rule to make any general statements about the weights of M&Ms. Also, calculate the percentage of M&Ms with weights between 0.802 and 0.946 grams using the Empirical Rule and determine the actual percentage in that range.

This problem demonstrates how to apply the Empirical Rule (68-95-99.7 rule) to interpret a histogram of M&M weights. We explore the appropriateness of the rule for bell-shaped distributions and calculate the percentage of M&Ms within specific weight ranges using the Empirical Rule.

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