To find the speed at which you should pull someone over, you'll need to determine the speed threshold that corresponds to the top 1% of speeds. This is typically found using z-scores in a normal distribution.
First, you need to find the z-score corresponding to the top 1% of speeds. This z-score can be found using a standard normal distribution table or a calculator. For the top 1% (which corresponds to the upper tail of the distribution), the z-score is approximately 2.33.
Now, use the formula for transforming a z-score to an actual value in a normal distribution:
X = μ + Z × σ
Where:
- X is the actual value (speed in this case)
- μ is the mean speed (68.3 mph)
- Z is the z-score (2.33)
- σ is the standard deviation (3.7 mph)
Plugging in the values:
X = 68.3 + 2.33 × 3.7
X ≈ 68.3 + 8.591 ≈ 76.891
Rounded to 1 decimal place, you should pull someone over if they are traveling at approximately 76.9 mph or faster.
