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)

Question

_______ watches

Answer 1

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

From the random sample of 400 watches, there are 3 defective watches. The proportion of defective watches in the sample is:

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

Now we need to apply this proportion to the total of 10,400 watches to estimate the number of defective watches:

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

Calculating it step by step:

1. Calculate the proportion: \[ \frac{3}{400} = 0.0075 \]

2. Multiply by the total number of watches: \[ 10,400 \times 0.0075 = 78 \]

Therefore, the expected number of defective watches in a total of 10,400 watches is:

\[ \boxed{78} \]