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?

Answer 1

To estimate the number of defective watches in a total population based on the sample data, we can use the proportion of defective watches found in the sample.

In the sample of 400 watches, there are 3 defective watches. The proportion of defective watches in the sample can be calculated as follows:

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

Now, we can use this proportion to estimate the number of defective watches in the total population of 10,400 watches.

\[ \text{Estimated number of defective watches} = \text{Total number of watches} \times \text{Proportion of defective watches} \]

Substituting the values:

\[ \text{Estimated number of defective watches} = 10,400 \times \frac{3}{400} \]

Calculating that gives:

\[ \text{Estimated number of defective watches} = 10,400 \times 0.0075 = 78 \]

So, based on the sample data, we would expect approximately 78 watches out of the total 10,400 to be defective.