According to the Empirical Rule, what percentages lie within 1, 2, and 3 standard deviations?

According to the Empirical Rule, what percentages lie within 1, 2, and 3 standard deviations?

• A. 50%, 75%, 100%
• B. 34%, 13.5%, 2.5%
• C. 68.26%, 95.45%, 99.73%
• D. 60%, 90%, 95%

Answer: (C)

In a normal distribution, most of the data cluster around the mean, and the Empirical Rule gives the approximate percentages of observations that fall within certain distances from the mean measured in standard deviations. The exact probabilities for a standard normal distribution are: about 68.26% lie within one standard deviation, about 95.45% lie within two standard deviations, and about 99.73% lie within three standard deviations. These precise values come from integrating the standard normal curve or using Z-tables. That’s why the right choice lists 68.26%, 95.45%, and 99.73%—they match the exact probabilities for the normal distribution. In practice, people often round to 68%, 95%, and 99.7% for ease of use. The other options don’t align with these central-normal percentages, so they don’t represent the empirical rule for a normal distribution.

In a normal distribution, most of the data cluster around the mean, and the Empirical Rule gives the approximate percentages of observations that fall within certain distances from the mean measured in standard deviations. The exact probabilities for a standard normal distribution are: about 68.26% lie within one standard deviation, about 95.45% lie within two standard deviations, and about 99.73% lie within three standard deviations. These precise values come from integrating the standard normal curve or using Z-tables.

That’s why the right choice lists 68.26%, 95.45%, and 99.73%—they match the exact probabilities for the normal distribution. In practice, people often round to 68%, 95%, and 99.7% for ease of use.

The other options don’t align with these central-normal percentages, so they don’t represent the empirical rule for a normal distribution.