Question

a company that produces only one type of item wants to estimate the percent of the itemsproduced in a typical week that are defective. a random sample of 260 of the itemsproduced in a certain week were tested. based on the sample, it is estimated that 8.75% ofall items produced by the company in this week are defective, with an associated margin oferror of 3.43%. based on the estimate and associated margin of error, which of the followingis the most appropriate conclusion about all items produced by the company during thisweek?a 3.43% of the items are defective.b it is plausible that between 5.32% and 12.18% of the items are defective.c 8.75% of the items are defective.d it is plausible that more than 12.18% of the items are defective.

Explanation:

Step1: Understand margin of error concept

The margin of error gives a range around the estimated percentage. The formula for the range is \( \text{Estimated percentage}-\text{Margin of error}\) to \( \text{Estimated percentage}+\text{Margin of error}\).

Step2: Calculate the lower and upper bounds

The estimated percentage of defective items is \(8.75\%\) and the margin of error is \(3.43\%\).
The lower bound is \(8.75\% - 3.43\%=5.32\%\).
The upper bound is \(8.75\%+ 3.43\% = 12.18\%\).

Answer:

B. It is plausible that between \(5.32\%\) and \(12.18\%\) of the items are defective.