The problem provides data for three drivers who participated in a race. It asks which driver had the fastest "typical race time." Here's the breakdown of the information given:

• Driver A: Mean race time = 4.01 seconds, Standard deviation = 0.05 seconds
• Driver B: Mean race time = 3.96 seconds, Standard deviation = 0.12 seconds
• Driver C: Mean race time = 3.99 seconds, Standard deviation = 0.19 seconds

The fastest "typical" race time considers both the mean (average) and the variability in performance (standard deviation). The driver with the lowest mean race time and the least variability (small standard deviation) is most likely to be the fastest consistently.

Explanation:

1. Driver A has the largest mean time (4.01 seconds) but the smallest variability (0.05 seconds). This means Driver A is quite consistent but slower on average.
2. Driver B has the smallest mean time (3.96 seconds) but higher variability (0.12 seconds), meaning that while they are the fastest on average, their times vary more.
3. Driver C has a mean time of 3.99 seconds and the highest variability (0.19 seconds), meaning their performance is less predictable and can fluctuate more.

Conclusion:

• Driver B has the fastest average time (mean of 3.96 seconds), which suggests that Driver B has the fastest typical race time despite having slightly higher variability.

Would you like further details or have any questions?

Related Questions:

1. How does standard deviation affect the typical race time?
2. Why is Driver A’s consistency important even though they have a slower mean time?
3. Can a driver with a higher standard deviation ever be considered "better"?
4. How could we use this data to predict future race outcomes?
5. What does "typical" race time mean in terms of statistics?

Tip:

In race data analysis, always look at both the mean and the standard deviation to get a complete picture of performance consistency.