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

0.0307%
0.0307%

90.3067%
90.3067%

−3.07%
negative 3.07 percent

3.07%

Answer 1

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

\[ \text{Percent Error} = \frac{\text{Estimated Value} - \text{Actual Value}}{\text{Actual Value}} \times 100 \]

In this case:

• Estimated Value (Layla's prediction) = 79,000
• Actual Value (full stadium capacity) = 81,500

Now, plug the values into the formula:

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

Calculating the numerator:

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

Now, substitute this into the formula:

\[ \text{Percent Error} = \frac{-2,500}{81,500} \times 100 \]

Calculating the fraction:

\[ \frac{-2,500}{81,500} \approx -0.0307 \]

Now multiply by 100 to convert to a percentage:

\[ -0.0307 \times 100 \approx -3.07% \]

Thus, the percent error of Layla’s prediction is \(-3.07%\).

So the correct answer is:

−3.07% (negative 3.07 percent)