Reaction Speed Test for Inexperienced Pilots

Overview: Inexperienced pilots participate in an online reaction speed test as part of their training program.

Mean Reaction Time: The average reaction time for the test is calculated to be:
- Value: 273 milliseconds

Standard Deviation: This is a measure of the amount of variation or dispersion of a set of values:
- Value: 82 milliseconds

Z-Score: A z-score represents the number of standard deviations a data point is from the mean.
- Formula for Z-Score: The z-score can be calculated using the formula:
  $z = \frac{(X - \mu)}{\sigma}$
- Where:
  - $z$ = z-score
  - $X$ = raw score (individual reaction time)
  - $\mu$ = mean
  - $\sigma$ = standard deviation

Given: Fiona Flyer's z-score = -0.9
Using the z-score formula:
- Rearranging the formula to find the raw score (Fiona's reaction time):
  $X = z * \sigma + \mu$
Substituting Values:
$X = (-0.9) * 82 + 273$
Calculating Fiona's Reaction Time:
- Compute:
  $X = -73.8 + 273$
  $X = 199.2 ext{ milliseconds}$
Final Value:
- Fiona's Reaction Time: 199.2 milliseconds

Condition: Tommy Takeoff's reaction time is stated to be the same amount of time away from the mean reaction time as Fiona's, but not equal to Fiona's time.
Explanation:
- This is possible because:
- The value of a negative z-score indicates that a reaction time is below the mean.
- Tommy's reaction time can be an equal distance from the mean but may fall on the opposite side (above the mean), resulting in a positive z-score.

Considering the absolute distance from mean:
- The distance for Fiona's z-score is:
  $|z| * \sigma = 0.9 * 82 = 73.8 ext{ milliseconds}$
Calculating Tommy's Reaction Time:
- Since Tommy is the same distance from the mean but positive:
- Thus, Tommy's reaction time can be calculated as:
  $\mu + |z| * \sigma = 273 + 73.8$
Final Calculation:
$273 + 73.8 = 346.8 ext{ milliseconds}$
Final Value:
- Tommy's Reaction Time: 346.8 milliseconds