Question

In a random sampling of 200 cars of a model, 3 have manufocturing dafects. If there is a direct variotion batween the number of cars and the number of defects, how meny of 10,000 cors of the same model will have a manufocturing defect?

Answer 1

If there is a direct variation between the number of cars and the number of defects, we can set up a proportion to estimate how many of 10,000 cars of the same model will have a manufacturing defect based on the information from the random sampling of 200 cars.

The proportion can be set up as follows:

(Defective cars in sample) / (Total cars in sample) = (Defective cars in the larger population) / (Total cars in the larger population)

So, in your case:

(3 defective cars in the sample) / (200 total cars in the sample) = (x defective cars in the larger population) / (10,000 total cars in the larger population)

Now, we can solve for 'x':

(3 / 200) = (x / 10,000)

To find 'x', first calculate the value of (3 / 200):

(3 / 200) = 0.015

Now, set up the equation:

0.015 = (x / 10,000)

To solve for 'x', multiply both sides by 10,000:

x = 0.015 * 10,000

x = 150

So, it is estimated that out of 10,000 cars of the same model, approximately 150 will have a manufacturing defect if there is a direct variation between the number of cars and the number of defects based on the random sampling of 200 cars.

Explanation: