A university football stadium has 81,500 seats. The stadium is at full capacity on game day. Layla believes only 79,000 seats are occupied. Find the percent error of Layla’s prediction. Round your answer to the nearest hundredth of a percent.(1 point)

Question

Responses

3.07%
3.07%

−3.07%
negative 3.07 percent

90.3067%
90.3067%

0.0307%
0.0307%

Answer 1

To calculate the percent error of Layla's prediction, we can use the formula for percent error:

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

In this case:

• The actual value (full capacity of the stadium) is 81,500 seats.
• The predicted value (Layla's belief) is 79,000 seats.

Using the formula:

\[ \text{Percent Error} = \left( \frac{81,500 - 79,000}{81,500} \right) \times 100 \]

Calculating the difference:

\[ 81,500 - 79,000 = 2,500 \]

Now plug that into the formula:

\[ \text{Percent Error} = \left( \frac{2,500}{81,500} \right) \times 100 \]

Calculating:

\[ \text{Percent Error} \approx 0.0307 \times 100 \approx 3.07% \]

Since this is a positive difference, the percent error is positive.

Thus, the answer is:

3.07%