Question

1 three drivers compete in the same 15 races. the mean and standard deviation for the race times of each of the drivers are given. driver a has a mean race time of 4.01 seconds and a standard deviation of 0.05 seconds. driver b has a mean race time of 3.96 seconds and a standard deviation of 0.12 seconds. driver c has a mean race time of 3.99 seconds and a standard deviation of 0.19 seconds. a. which driver has the fastest typical race time? b. which driver’s race times are the most variable? c. which driver do you predict will win the next race? support your prediction using the mean and standard deviation.

Explanation:

Part a

Step1: Recall mean as typical time

Mean represents typical value. Compare means: Driver A: 4.01, Driver B: 3.96, Driver C: 3.99.

Step2: Identify smallest mean

Smallest mean (fastest typical time) is 3.96 (Driver B).

Step1: Recall standard deviation meaning

Standard deviation (SD) measures variability. Higher SD means more variable.

Step2: Compare SDs

Driver A: 0.05, Driver B: 0.12, Driver C: 0.19. Largest SD is 0.19 (Driver C).

Step1: Analyze mean (speed)

Lower mean = faster typical time. Driver B (3.96) < Driver C (3.99) < Driver A (4.01).

Step2: Analyze standard deviation (consistency)

Lower SD = more consistent. Driver A: 0.05, Driver B: 0.12, Driver C: 0.19. Driver B is fast (low mean) and moderately consistent. Driver A is consistent but slower. Driver C is variable.

Step3: Predict winner

Driver B has the fastest mean and reasonable consistency, so likely to win.

Answer:

Driver B

Part b