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Math  /  Data & Statistics

QuestionManaged Favorites PCPS Desktop Mc Graw Percent Error ⋅\cdot Practice Question 6 of 14
Question 6 A cyclist estimates that he will bike 80 miles this week. He actually bikes 75.5 miles. What is the percent error of the cyclist's estima Round the percent to the nearest hundredth if necessary. \% □\square (5) Need help with this question?

Studdy Solution

STEP 1

1. The estimated distance is 80 miles.
2. The actual distance biked is 75.5 miles.
3. Percent error is calculated using the formula:
Percent Error=(∣Estimated Value−Actual Value∣Estimated Value)×100\text{Percent Error} = \left( \frac{|\text{Estimated Value} - \text{Actual Value}|}{\text{Estimated Value}} \right) \times 100

STEP 2

1. Calculate the absolute error.
2. Calculate the percent error.
3. Round the percent error to the nearest hundredth.

STEP 3

Calculate the absolute error:
∣Estimated Value−Actual Value∣=∣80−75.5∣=4.5|\text{Estimated Value} - \text{Actual Value}| = |80 - 75.5| = 4.5

STEP 4

Calculate the percent error using the formula:
Percent Error=(4.580)×100\text{Percent Error} = \left( \frac{4.5}{80} \right) \times 100
Calculate the division:
4.580=0.05625\frac{4.5}{80} = 0.05625
Multiply by 100 to convert to a percentage:
0.05625×100=5.6250.05625 \times 100 = 5.625

STEP 5

Round the percent error to the nearest hundredth:
5.625≈5.635.625 \approx 5.63
The percent error is:
5.63% \boxed{5.63\%}

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