Let's analyze the given contingency table to determine the marginal distributions for gold and diamonds.
[tex]\[
\begin{tabular}{|l|c|c|c|}
\hline
Ornaments & Gold & Diamond & Total \\
\hline
Necklace & 532 & 689 & 1221 \\
\hline
Ring & 131 & 482 & 613 \\
\hline
Total & 663 & 1171 & 1834 \\
\hline
\end{tabular}
\][/tex]
### Marginal Distribution for Gold
The marginal distribution for gold means summing up all the counts of gold items irrespective of their type (necklace or ring).
- Number of gold necklaces: 532
- Number of gold rings: 131
- Total number of gold items: 532 + 131 = 663
So, the marginal distribution for gold is:
- 532 for necklaces
- 131 for rings
- 663 in total
### Marginal Distribution for Diamonds
The marginal distribution for diamonds means summing up all the counts of diamond items, again irrespective of their type (necklace or ring).
- Number of diamond necklaces: 689
- Number of diamond rings: 482
- Total number of diamond items: 689 + 482 = 1171
So, the marginal distribution for diamonds is:
- 689 for necklaces
- 482 for rings
- 1171 in total
Thus, the marginal distributions, expressed separately for gold and diamond items, are as follows:
1. Gold items:
- Necklaces: 532
- Rings: 131
- Total: 663
2. Diamond items:
- Necklaces: 689
- Rings: 482
- Total: 1171
### Selections
Based on the given question, the appropriate selections for the marginal distributions should include:
- 532 (Gold necklaces)
- 131 (Gold rings)
- 663 (Total gold items)
- 689 (Diamond necklaces)
- 482 (Diamond rings)
- 1171 (Total diamond items)
These values represent the marginal distributions for both gold and diamond ornaments according to the contingency table provided.
