6.) in international swimming, the mean time for the mens $100\\text{ m}$ freestyle is $50.46\\text{ sec}$…

6.) in international swimming, the mean time for the mens $100\\text{ m}$ freestyle is $50.46\\text{ sec}$ with a standard deviation of $0.6\\text{ sec}$. for the $200\\text{ m}$ freestyle, the mean time is $110.4\\text{ sec}$ with a standard deviation of $1.4\\text{ sec}$. jasons best time for the $100\\text{ m}$ is $48.76\\text{ sec}$ and for the $200\\text{ m}$ is $108.43\\text{ sec}$. if he can only enter one of these events in the competition, which one should he enter?

6.) in international swimming, the mean time for the mens $100\\text{ m}$ freestyle is $50.46\\text{ sec}$ with a standard deviation of $0.6\\text{ sec}$. for the $200\\text{ m}$ freestyle, the mean time is $110.4\\text{ sec}$ with a standard deviation of $1.4\\text{ sec}$. jasons best time for the $100\\text{ m}$ is $48.76\\text{ sec}$ and for the $200\\text{ m}$ is $108.43\\text{ sec}$. if he can only enter one of these events in the competition, which one should he enter?

Answer

Explanation:

Step1: Identify the formula for z-score

$$z = \frac{x - \mu}{\sigma}$$

Step2: Calculate z-score for 100 m freestyle

$$z_{100} = \frac{48.76 - 50.46}{0.6} = \frac{-1.70}{0.6} \approx -2.833$$

Step3: Calculate z-score for 200 m freestyle

$$z_{200} = \frac{108.43 - 110.4}{1.4} = \frac{-1.97}{1.4} \approx -1.407$$

Step4: Compare z-scores for better performance

In racing, a lower (more negative) z-score indicates a time further below the mean, representing a better relative performance.

Answer:

Jason should enter the 100 m freestyle because his z-score of -2.833 is lower than his z-score of -1.407 for the 200 m freestyle, indicating a better relative performance.