Sure! Let’s break down the problem step by step and provide a clear solution.
1. Identify the observed frequency for item 2 produced by Plant B:
- From the given table, we can clearly see that Plant B produces 12 units of item 2 per day.
- Therefore, the observed frequency for item 2 at Plant B is 12 units.
2. Calculate the total number of items produced per day by each plant:
- For Plant A:
- Item 1: 22 units
- Item 2: 8 units
- Item 3: 14 units
Total production at Plant A = 22 + 8 + 14 = 44 units
- For Plant B:
- Item 1: 15 units
- Item 2: 12 units
- Item 3: 25 units
Total production at Plant B = 15 + 12 + 25 = 52 units
3. Calculate the total production of item 2 across both plants:
- Item 2 produced by Plant A = 8 units
- Item 2 produced by Plant B = 12 units
Total production of item 2 = 8 + 12 = 20 units
4. Calculate the overall total production of all items across both plants:
- Total production at Plant A = 44 units
- Total production at Plant B = 52 units
Overall total production of all items = 44 + 52 = 96 units
5. Calculate the expected frequency for item 2 produced by Plant B:
- The formula to calculate the expected frequency:
[tex]\[
\text{Expected frequency for item 2 at Plant B} = \left( \frac{\text{Total production of item 2}}{\text{Overall total production of all items}} \right) \times \text{Total production at Plant B}
\][/tex]
- Plugging in the values:
[tex]\[
\text{Expected frequency for item 2 at Plant B} = \left( \frac{20}{96} \right) \times 52 \approx 10.8333 \text{ units}
\][/tex]
Summary and Final Results:
- Observed frequency for item 2 produced by Plant B = 12 units.
- Expected frequency for item 2 produced by Plant B ≈ 10.8333 units.
Therefore, the observed and expected frequencies for item 2 produced by Plant B are 12 units and approximately 10.8333 units, respectively.
