Pregunta
Multiple Choice Question
Randall Racer runs the 100 meter dash in an average time of 10.4 seconds with a standard deviation of 0.1 seconds. If Randall’s times are normally distributed, we
have a
Randall Racer runs the 100 meter dash in an average time of 10.4 seconds with a standard deviation of 0.1 seconds. If Randall’s times are normally distributed, we
have a
Ask by Cummings Estrada. in the United States
Jan 25,2025
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There is a 99.7% chance that Randall’s next race time will be greater than 10.1 seconds.
Solución
To determine the value below which Randall’s finishing time will not fall with a 99.7% probability, we can use the Empirical Rule (also known as the 68-95-99.7 rule) for normally distributed data.
Given:
- Mean (μ): 10.4 seconds
- Standard Deviation (σ): 0.1 seconds
- Confidence Level: 99.7%
Empirical Rule Insights:
- 68% of data falls within ±1σ of the mean.
- 95% of data falls within ±2σ of the mean.
- 99.7% of data falls within ±3σ of the mean.
For a 99.7% confidence interval:
- The lower bound is calculated as μ - 3σ.
Interpretation:
- There is a 99.7% probability that Randall’s finishing time will be greater than 10.1 seconds in his next race.
Answer:
10.1 seconds
10.1 seconds
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Simplifique esta solución Bonus Knowledge
To determine the time which Randall Racer is expected to finish his next race with a
Now, let’s dive into a little historical context! The 100 meter dash has been a defining event in various athletic competitions, including the Olympics, since its inception in the late 19th century. The sprint showcases not just speed but also technique, agility, and explosive power, making it a spectacular and competitive event!
For some practical advice, if you ever find yourself training for a sprint, focus on your starting block technique and driving phase, as these are crucial for optimizing your race times. A common mistake athletes make is neglecting their recovery—you need to give your muscles time to repair and grow stronger. Embrace rest as much as you embrace training!
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