In a random sample of 400 watches, 3 are defective. Out of a total of 10,400 watches, how many would you expect to be defective based on this sample data?(1 point)

Answer 1

To find the expected number of defective watches in a total of 10,400 watches based on the sample data, you can use the proportion of defective watches found in the sample.

In the sample of 400 watches, there were 3 defective watches. The proportion of defective watches is:

\[ \text{Proportion of defective watches} = \frac{\text{Number of defective watches}}{\text{Total number of watches in sample}} = \frac{3}{400} \]

Now, to find the expected number of defective watches in the total of 10,400 watches, multiply this proportion by the total number of watches:

\[ \text{Expected number of defective watches} = \left(\frac{3}{400}\right) \times 10,400 \]

Calculating that gives:

\[ \frac{3 \times 10,400}{400} = \frac{31,200}{400} = 78 \]

So, you would expect 78 defective watches in a total of 10,400 watches.