Question

4.4 ps - 18
the dot plot shows predictions for the winning time in the 200 - meter sprint. the winner
finished the race in 22.5 seconds. what is the greatest percent error among
the predictions?
the greatest percent error among the predictions is %
(round to the nearest tenth as needed.)

Explanation:

Step1: Recall the percent - error formula

The percent - error formula is \( \text{Percent Error}=\frac{\vert\text{Estimated Value}-\text{Actual Value}\vert}{\text{Actual Value}}\times100\%\). The actual value is \(22.5\) seconds.

Step2: Find the estimated values from the dot - plot

The estimated values from the dot - plot are \(22.2\), \(22.3\), \(22.4\), \(22.5\), \(22.6\), \(22.7\), \(22.8\), \(22.9\)

Step3: Calculate the absolute differences

For \(22.2\): \(\vert22.2 - 22.5\vert=\vert- 0.3\vert = 0.3\)
For \(22.3\): \(\vert22.3 - 22.5\vert=\vert-0.2\vert = 0.2\)
For \(22.4\): \(\vert22.4 - 22.5\vert=\vert-0.1\vert = 0.1\)
For \(22.5\): \(\vert22.5 - 22.5\vert=0\)
For \(22.6\): \(\vert22.6 - 22.5\vert = 0.1\)
For \(22.7\): \(\vert22.7 - 22.5\vert=0.2\)
For \(22.8\): \(\vert22.8 - 22.5\vert=0.3\)
For \(22.9\): \(\vert22.9 - 22.5\vert = 0.4\)

Step4: Calculate the percent errors

Using the formula \( \text{Percent Error}=\frac{\vert\text{Estimated Value}-\text{Actual Value}\vert}{\text{Actual Value}}\times100\%\)
For the estimated value of \(22.9\):

$$
LATEXBLOCK0
$$

Answer:

\(1.8\)