Question

In a certain sporting goods manufacturing company, a quality control expert tests a randomly selected group of 1,000 tennis balls in order to determine how many contain defects. If this quality control expert discovered that 13 of the randomly selected tennis balls were defective, which of the following inferences would be most supported? A) \(98.7 \%\) of the company's tennis balls are defective. B) \(98.7 \%\) of the company's tennis balls are not defective. C) \(9.87 \%\) of the company's tennis balls are defective. D) \(9.87 \%\) of the company's tennis balls are not defective.

Short answer

The correct inference is option B) 98.7% of the company's tennis balls are not defective.

Step-by-step solution

Understand the given information

We are given a sample of 1,000 tennis balls, and out of which 13 balls are found to be defective.

Calculate the percentage of defective tennis balls

To find the percentage of defective tennis balls, we need to divide the number of defective balls by the total number of balls tested and then multiply by 100. Defective Percentage = \(\frac{13}{1000} * 100\)

Perform the calculation

Defective Percentage = \(\frac{13}{1000} * 100 = 1.3\%\) of tennis balls are defective.

Calculate the percentage of non-defective tennis balls

Since we know the percentage of defective tennis balls, we can subtract it from 100% to find the percentage of non-defective tennis balls. Non-defective Percentage = 100% - Defective Percentage = 100% - 1.3% = 98.7% Thus, 98.7% of tennis balls are non-defective.

Identify the correct inference

Using our calculations, we can choose the correct answer: A) 98.7% of the company's tennis balls are defective. (Incorrect) B) 98.7% of the company's tennis balls are not defective. (Correct) C) 9.87% of the company's tennis balls are defective. (Incorrect) D) 9.87% of the company's tennis balls are not defective. (Incorrect) The correct inference is option B) 98.7% of the company's tennis balls are not defective.