What percentage of observations fall within three standard deviations of the mean in a normal distribution?

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Multiple Choice

What percentage of observations fall within three standard deviations of the mean in a normal distribution?

Explanation:
Think about the Empirical Rule for a normal distribution. It shows how data spread around the mean: about 68% lie within one standard deviation, about 95% within two standard deviations, and about 99.7% within three standard deviations. So within three standard deviations, roughly 99.7% of observations occur, leaving only about 0.3% outside that range (about 0.15% in each tail). That’s why 99.7% is the correct choice. The other numbers correspond to smaller intervals: 68% for ±1σ and 95% for ±2σ; 99% isn’t the standard value tied to ±3σ.

Think about the Empirical Rule for a normal distribution. It shows how data spread around the mean: about 68% lie within one standard deviation, about 95% within two standard deviations, and about 99.7% within three standard deviations. So within three standard deviations, roughly 99.7% of observations occur, leaving only about 0.3% outside that range (about 0.15% in each tail). That’s why 99.7% is the correct choice. The other numbers correspond to smaller intervals: 68% for ±1σ and 95% for ±2σ; 99% isn’t the standard value tied to ±3σ.

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