Question

Set up the following word problem as a proportion and solve. You must show your work to receive full credit. In a random sample of 400 cars of a particular model, 5 have a manufacturing defect. At this rate, how many of 10,000 cars of the same model will have a manufacturing defect? please label your answer.

Answer 1

At the rate expected, 125 of the 10,000 cars from said manufacturer will contain a defect.

Explanation:

Given a sample size of 400, this will be a representation of the total of all cars from this manufacturer.

If 5 of these cars have been found to have a defect, then the rate of defects within the company's cars is expected to be

5/400

Using this proportion to expand to a sample size of 10,000 cars then, we can create the expression

5/400 = x/10,000 Multiply both sides by 10,000 to isolate x

50,000/400 = x Reduce the fraction

125 = x

Therefore, within a sample of 10,000 cars from said manufacturer, it can be expected that 125 of these vehicles will have a defect.