Question
4) McKinley Middle School held a canned food drive for a local food pantry. Before the drive, the principal predicted the students would collect 600 cans of food, but he was pleasantly surprised when they collected 750 cans. What is the percent error for the principal's prediction? (1) If necessary, round your answer to the nearest tenth of a percent. Submit
Ask by Byrd Clarke. in the United States
Jan 24,2025
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Tutor-Verified Answer
Answer
The percent error for the principal's prediction is 25.0%.
Solution
To calculate the **percent error** for the principal's prediction, use the following formula:
\[
\text{Percent Error} = \left( \frac{|\text{Observed} - \text{Predicted}|}{|\text{Predicted}|} \right) \times 100\%
\]
**Given:**
- **Predicted** number of cans: 600
- **Observed** number of cans: 750
**Calculation:**
\[
\text{Percent Error} = \left( \frac{|750 - 600|}{600} \right) \times 100\% = \left( \frac{150}{600} \right) \times 100\% = 0.25 \times 100\% = 25\%
\]
Since the problem asks to round to the nearest tenth of a percent if necessary, the final answer is:
**25.0%**
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Bonus Knowledge
To find the percent error, you can use the formula: \[ \text{Percent Error} = \left( \frac{\text{Actual Value} - \text{Predicted Value}}{\text{Predicted Value}} \right) \times 100 \] In this case, the actual value is 750 cans and the predicted value is 600 cans. Plugging in the numbers: \[ \text{Percent Error} = \left( \frac{750 - 600}{600} \right) \times 100 = \left( \frac{150}{600} \right) \times 100 = 25\% \] Thus, the percent error for the principal's prediction is 25.0%.