To determine the mean number of orange M&Ms in the small bags that passed quality control, let's follow the steps below:
1. Identify the bags that pass quality control: A bag passes quality control if it has at least 6 orange M&Ms. From the given table, these are the bags containing 6, 7, and 8 orange M&Ms.
2. Extract frequencies corresponding to the passing bags:
- Bags with 6 orange M&Ms: frequency = 71
- Bags with 7 orange M&Ms: frequency = 38
- Bags with 8 orange M&Ms: frequency = 37
3. Calculate the total number of bags that passed quality control:
[tex]\[
\text{Total passing bags} = 71 + 38 + 37 = 146.
\][/tex]
4. Calculate the weighted sum of orange M&Ms in the passing bags:
- For 6 orange M&Ms: [tex]\(6 \times 71 = 426\)[/tex]
- For 7 orange M&Ms: [tex]\(7 \times 38 = 266\)[/tex]
- For 8 orange M&Ms: [tex]\(8 \times 37 = 296\)[/tex]
[tex]\[
\text{Weighted sum} = 426 + 266 + 296 = 988.
\][/tex]
5. Calculate the mean number of orange M&Ms in the passing bags:
[tex]\[
\text{Mean} = \frac{\text{Weighted sum}}{\text{Total passing bags}} = \frac{988}{146} \approx 6.767.
\][/tex]
Hence, the mean number of orange M&Ms in the bags that passed quality control is approximately 6.8. The correct answer is:
D. 6.8
