in an outdoor experiment, mich is testing his football robot kicking a ball and hitting the goal.She obtained 4 trials measuring the velocity of the ball. The measurement are summarized below.
Trial 1: 4.71 m/s2 
Trial 2: 5.08 m/s2 
Trial 3: 5.21 m/s2 
Trial 4: 4.81 m/s2 

What is the percentage of precision of the robot?


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To calculate the percentage precision of the robot in Mich's experiment, we need to use the formula for percentage precision, which is related to the spread (or consistency) of the measured values around the mean.

The formula for percentage precision is:

\[
\text{Percentage Precision} = \left(1 - \frac{\text{Standard Deviation}}{\text{Mean}}\right) \times 100\%
\]

### Step 1: Calculate the Mean Velocity
The mean velocity is calculated by averaging the velocities from all four trials.

Given:
- Trial 1: 4.71 m/s²
- Trial 2: 5.08 m/s²
- Trial 3: 5.21 m/s²
- Trial 4: 4.81 m/s²

The mean \( \bar{x} \) is given by:

\[
\bar{x} = \frac{4.71 + 5.08 + 5.21 + 4.81}{4}
\]

### Step 2: Calculate the Standard Deviation
The standard deviation measures the dispersion of the velocities from the mean. The formula for the standard deviation \( \sigma \) for a sample is:

\[
\sigma = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n-1}}
\]

Where \( x_i \) are the individual velocity measurements and \( n \) is the number of trials.

### Step 3: Calculate the Percentage Precision
Finally, we'll calculate the percentage precision using the formula:

\[
\text{Percentage Precision} = \left(1 - \frac{\sigma}{\bar{x}}\right) \times 100\%
\]

Now, let's compute these values.### Complete Solution:

1. **Mean Velocity Calculation:**
   \[
   \bar{x} = \frac{4.71 + 5.08 + 5.21 + 4.81}{4} = 4.9525 \, \text{m/s}^2
   \]

2. **Standard Deviation Calculation:**
   \[
   \sigma = 0.2321 \, \text{m/s}^2
   \]

3. **Percentage Precision Calculation:**
   \[
   \text{Percentage Precision} = \left(1 - \frac{0.2321}{4.9525}\right) \times 100\% \approx 95.31\%
   \]

### Conclusion:
The percentage precision of Mich's football robot is approximately **95.31%**.

Do you need further details or have any questions?

### Related Questions:
1. What is the significance of a high percentage precision in experiments?
2. How does standard deviation influence the overall precision of a system?
3. If one trial's velocity measurement was significantly different, how would that affect precision?
4. What would be the percentage precision if all trials had identical velocities?
5. How can the robot's kicking mechanism be improved to increase precision?

### Tip:
In experiments, improving the consistency of repeated measurements often leads to better precision, even if the accuracy (closeness to the true value) might need separate improvements.

In an outdoor experiment, Mich is testing his football robot kicking a ball and hitting the goal. She obtained 4 trials measuring the velocity of the ball. The measurements are summarized below. Trial 1: 4.71 m/s², Trial 2: 5.08 m/s², Trial 3: 5.21 m/s², Trial 4: 4.81 m/s². What is the percentage of precision of the robot?

Learn how to calculate the percentage precision of a football robot in an outdoor experiment by measuring the ball's velocity in four trials. This problem involves statistical concepts such as mean, standard deviation, and percentage precision, making it suitable for students in Grades 9-12.

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