When using the 2-sigma rule, if 75% fall within ±2 SD, what percentage lies outside this range?

When using the 2-sigma rule, if 75% fall within ±2 SD, what percentage lies outside this range?

• A. 25%
• B. 50%
• C. 0%
• D. 75%

Answer: (A)

The idea is simple: the percentages inside and outside the interval must add up to 100%. If 75% fall within ±2 SD, then the remaining observations lie outside. 100% minus 75% equals 25%. So, outside this range is 25%. Note: the familiar empirical rule says about 95% lie within ±2 SD for a normal distribution, leaving about 5% outside. This question uses a given 75% inside, which would imply 25% outside, regardless of the usual rule.

The idea is simple: the percentages inside and outside the interval must add up to 100%. If 75% fall within ±2 SD, then the remaining observations lie outside. 100% minus 75% equals 25%. So, outside this range is 25%.

Note: the familiar empirical rule says about 95% lie within ±2 SD for a normal distribution, leaving about 5% outside. This question uses a given 75% inside, which would imply 25% outside, regardless of the usual rule.