Question

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? Round your answer to the nearest whole number.(1 point) watches

Answer 1

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

From the sample:

- Number of defective watches = 3
- Total number of watches in the sample = 400

The proportion of defective watches in the sample is:

\[
\text{Proportion of defective watches} = \frac{3}{400}
\]

To find the expected number of defective watches in the total population of 10,400, you can multiply this proportion by the total number of watches:

\[
\text{Expected number of defective watches} = \text{Proportion of defective watches} \times \text{Total number of watches in the population}
\]

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

Calculating that:

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

Therefore, you would expect approximately **78** defective watches in the total population.