Final answer:
To use the theoretical distribution to find the IQR, percentiles, and median, calculate the mean and standard deviation of the sample data, use the z-distribution for percentiles, and calculate actual values based on these z-scores. The 85th percentile represents the value below which 85% of the data falls.
Step-by-step explanation:
To use the theoretical distribution to find various statistical measures like the IQR, percentiles, and median, you can follow these general steps
The meaning of the 85th percentile of this distribution is that 85% of the values lie below this point, and 15% lie above it.
Example:
If the mean lap time is 120 seconds and the standard deviation is 5 seconds, and you want to find the 85th percentile:
This means that 85% of the lap times are expected to be less than 125.2 seconds.