In a normal distribution, what percentage lies within three standard deviations of the mean?

In a normal distribution, what percentage lies within three standard deviations of the mean?

• A. 68.3%
• B. 75%
• C. 99.8%
• D. 95.4%

Answer: (C)

In a normal distribution, the Empirical Rule says about 68% fall within one standard deviation, about 95% within two, and about 99.7% within three. That means nearly all data lie within three standard deviations of the mean, with around 0.3% outside. The exact figure is 99.73%, so rounding to one decimal place commonly yields 99.7% or 99.8%. Saying 99.8% is the closest rounded value to the true proportion, which is why it’s the best match. The other options correspond to smaller ranges: 68.3% is within one SD, 95.4% within two SD, and 75% is not a standard interval in this rule.

In a normal distribution, the Empirical Rule says about 68% fall within one standard deviation, about 95% within two, and about 99.7% within three. That means nearly all data lie within three standard deviations of the mean, with around 0.3% outside. The exact figure is 99.73%, so rounding to one decimal place commonly yields 99.7% or 99.8%. Saying 99.8% is the closest rounded value to the true proportion, which is why it’s the best match. The other options correspond to smaller ranges: 68.3% is within one SD, 95.4% within two SD, and 75% is not a standard interval in this rule.