Question

lesson 13 practice problems
1 three drivers compete in the same fifteen - 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 0.16 seconds.
driver b has a mean race time of 3.96 seconds and a standard deviation of 0.17 seconds.
driver c has a mean race time of 3.93 seconds and a standard deviation of 0.19 seconds.
a. which driver has the fastest typical race time?
b. which drivers 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:

Step1: Compare mean times

The lower the mean race - time, the faster the typical race time. Driver A has a mean of 4.01 seconds, Driver B has a mean of 3.96 seconds, and Driver C has a mean of 3.93 seconds. Since 3.93<3.96<4.01, Driver C has the fastest typical race time.

Step2: Compare standard deviations

The larger the standard deviation, the more variable the data. Driver A has a standard deviation of 0.05 seconds, Driver B has a standard deviation of 0.12 seconds, and Driver C has a standard deviation of 0.15 seconds. Since 0.15 > 0.12>0.05, Driver C's race times are the most variable.

Step3: Make a prediction

Driver C has the fastest mean time, but also the highest variability. Driver B has a relatively fast mean time (3.96 seconds) and a lower variability (standard deviation of 0.12 seconds) compared to Driver C. A lower - variability driver is more consistent. So, Driver B is a good prediction to win the next race as they are likely to be more consistent around their relatively fast mean time.

Answer:

a. Driver C
b. Driver C
c. Driver B. Driver C has the fastest mean time but high variability. Driver B has a fast mean time and lower variability, indicating more consistency.