To determine the expected number of defective watches in a total of 10,400 watches based on the sample data, we first need to calculate the proportion of defective watches in the sample.
In the sample of 400 watches, there are 3 defective watches. Therefore, the proportion of defective watches is:
\[ \text{Proportion of defective watches} = \frac{\text{Number of defective watches}}{\text{Total number of watches in sample}} = \frac{3}{400} \]
Next, we calculate the expected number of defective watches in the total population of 10,400 watches using this proportion:
\[ \text{Expected number of defective watches} = \text{Proportion of defective watches} \times \text{Total number of watches} = \frac{3}{400} \times 10400 \]
Now, we perform the multiplication:
\[ \text{Expected number of defective watches} = \frac{3 \times 10400}{400} \]
Calculating \(3 \times 10400\):
\[ 3 \times 10400 = 31200 \]
Now divide by 400:
\[ \frac{31200}{400} = 78 \]
Thus, the expected number of defective watches in a total of 10,400 watches is:
\[ \boxed{78} \]