Question

Julian and Brittany mailed 275 wedding invitations to family and friends and predicted that they would all attend. Only 265 out of 275 people committed to attending the wedding. Calculate the percent error in their prediction. Round your answer to the nearest hundredth percent

Answer 1

To calculate the percent error in Julian and Brittany's prediction, we can use the following formula for percent error:

\[
\text{Percent Error} = \left( \frac{\text{Actual Value} - \text{Predicted Value}}{\text{Predicted Value}} \right) \times 100
\]

In this case:

- Predicted Value = 275 (the number of invitations mailed)
- Actual Value = 265 (the number of people who committed to attending)

Substituting the values into the formula:

\[
\text{Percent Error} = \left( \frac{265 - 275}{275} \right) \times 100
\]

Calculating the numerator:

\[
265 - 275 = -10
\]

Now substituting into the formula:

\[
\text{Percent Error} = \left( \frac{-10}{275} \right) \times 100
\]

Calculating the fraction:

\[
\frac{-10}{275} \approx -0.03636
\]

Now multiplying by 100 to convert it to a percentage:

\[
\text{Percent Error} \approx -0.03636 \times 100 \approx -3.636
\]

Rounding to the nearest hundredth percent:

\[
\text{Percent Error} \approx -3.64\%
\]

Since percent error is generally reported as a positive value representing the deviation from the expected result, we can say:

\[
\text{Percent Error} \approx 3.64 \%
\]

Thus, the percent error in their prediction is approximately **3.64%**.