A random sample of 200 widgets was tested from the 5,913 widgets produced by a factory in one day. If 41 of the sampled widgets were defective, approximately how many widgets produced in the factory that day would be expected to be defective?

The problem involves calculating defective widgets based on a random sample. The percentage of defective widgets in the sample is found to be 20.5%. By applying this percentage to the total production, we predict that almost 1212 units could be defective.

Explanation:

In a problem dealing with random samples and probabilities, you first need to understand your sample ratio. Here, the ratio of defective widgets to the total number tested is 41 defective out of 200, which proportions to 20.5%. It means that, within your sample, about 20.5% of the widgets were defective.

To understand how this might translate to the entire population of widgets (5,913), you can multiply that ratio (0.205) by the total number of widgets to get an approximate expected number of defective widgets produced that day, which would be about 1212 defective widgets (rounded).

Learn more about sample proportions here:

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