Question

Twenty percent of all telephones of a certain type are ________?

Answer 1

Twenty percent of all telephones of a certain type are defective.

Step-by-step explanation:

In a statistical context, when we encounter the phrase "Twenty percent," it refers to a proportion or percentage of the total. In this case, it signifies the defect rate among telephones of a specific type. To express this mathematically, let
`\( D \)` represent the number of defective phones and
`\( T \)` represent the total number of phones. The defect rate is given by the formula
`\( (D)/(T) * 100\% \)`. Given that twenty percent of the phones are defective, we can write this as
`\( (D)/(T) = (20)/(100) \).` To find the defective phones, we can rearrange the equation to
`\( D = 0.2 * T \)`.

Now, let's consider the practical implications of this result. If, for example, there are 500 phones of this type in circulation, the number of defective phones would be
`\( D = 0.2 * 500 = 100 \)`. This means that 100 phones out of the total 500 are defective. Such insights are crucial for quality control and ensuring customer satisfaction. It also allows for strategic decision-making, such as whether to improve manufacturing processes to reduce defects or to enhance post-production inspection.

In conclusion, understanding the percentage of defective phones provides a clear insight into the quality of the product. The ability to express this information both mathematically and practically is essential for informed decision-making in manufacturing, quality assurance, and customer service.