Question

brianna is a manager for a clothing store and sometimes finds merchandise to be damaged with stains, missing buttons, or broken zippers. based on the past, she estimates that 18 pieces of clothing being delivered to her store will be damaged this month. however, only 14 were actually damaged. what is the percent error of briannas estimate? round to the nearest percent (no decimal).

Explanation:

Step1: Calculate the absolute error

The formula for absolute error is \(| \text{Estimated value}-\text{Actual value}|\). Here, the estimated value is \(18\) and the actual value is \(14\). So, \(|18 - 14|=4\).

Step2: Calculate the percent error

The formula for percent error is \(\frac{\text{Absolute error}}{\text{Actual value}}\times100\%\). Substitute the absolute error (\(4\)) and actual value (\(14\)) into the formula: \(\frac{4}{14}\times 100\%=\frac{400}{14}\%\approx 28.57\%\).

Step3: Round to the nearest percent

Rounding \(28.57\%\) to the nearest percent gives \(29\%\).

Answer:

\(29\%\)