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%.
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