To solve the problem, we need to refer to the Empirical Rule, which states that for a normal distribution:
- Approximately 68% of the data falls within one standard deviation (±1σ) of the mean.
- Approximately 95% falls within two standard deviations (±2σ).
- Approximately 99.7% falls within three standard deviations (±3σ).
In this case, the mean (\( \mu \)) is 20 minutes, and the standard deviation (\( \sigma \)) is 5 minutes.
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Determine the range for one standard deviation:
- One standard deviation above the mean: \( 20 + 5 = 25 \) minutes
- One standard deviation below the mean: \( 20 - 5 = 15 \) minutes
Thus, approximately 68% of players complete the level between 15 and 25 minutes.
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Determine the range for two standard deviations:
- Two standard deviations above the mean: \( 20 + 2 \times 5 = 30 \) minutes
- Two standard deviations below the mean: \( 20 - 2 \times 5 = 10 \) minutes
Therefore, approximately 95% of players complete the level between 10 and 30 minutes.
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Calculate the percentage of players in the range between 25 and 30 minutes:
- From the Empirical Rule, we know that 68% of players fall between 15 and 25 minutes, and an additional 27% fall between 25 and 30 minutes (which is half of the remaining 32% from the full range of 10 to 30 minutes: \( 32% / 2 = 16% \)).
- Therefore, the percentage of players that falls between 25 and 30 minutes is 16%.
So, the total percentage of players completing the level in more than 25 minutes but less than 30 minutes (25 to 30 minutes) is approximately:
\[ \text{Percentage from 25 to 30 minutes} = 16% \]
Since we want to find the percentage of players completing it in "more than 25 minutes" (which gives us the interval from 25 to 30 minutes), the relevant amount is:
\[ \text{Percentage} = 16% \]
This value is not among the options (A, B, C, or D) provided. Please ensure that the question is accurately stated or that the options provided correspond to a different calculation needed.
However, based on the interpretations and standard calculations, the answer that best applies from what we've derived is not present in the given list. If you were asking specifically for a percentage directly related to scores falling just above 25 and up to 30 minutes, based on our calculations, looking for a bounded method would suggest option C (34%) as the next closest available percent that might discernibly represent that interval when all drawing from estimated partitions given those scores.
Please let me know if anything needs reconsideration or different methodology employed!
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