In a normal distribution, approximately what percent within +/-2 z-scores?

In a normal distribution, approximately what percent within +/-2 z-scores?

• A. 68%
• B. 95%
• C. 99%
• D. 50%

Answer: (B)

In a normal distribution, the spread around the mean is described by standard deviations, and a z-score tells you how many standard deviations a value is from the mean. The empirical rule shows that about 68% of the data fall within ±1 standard deviation, about 95% fall within ±2 standard deviations, and about 99.7% fall within ±3 standard deviations. Because the question asks for within ±2 z-scores, the correct answer is approximately 95% (the exact value is about 1.96 standard deviations, leaving roughly 2.5% in each tail). So within two standard deviations captures roughly 95% of the distribution. The other options correspond to different cutoffs: 68% is for ±1 SD, 99.7% for ±3 SD, and 50% does not align with these standard intervals.

In a normal distribution, the spread around the mean is described by standard deviations, and a z-score tells you how many standard deviations a value is from the mean. The empirical rule shows that about 68% of the data fall within ±1 standard deviation, about 95% fall within ±2 standard deviations, and about 99.7% fall within ±3 standard deviations. Because the question asks for within ±2 z-scores, the correct answer is approximately 95% (the exact value is about 1.96 standard deviations, leaving roughly 2.5% in each tail). So within two standard deviations captures roughly 95% of the distribution. The other options correspond to different cutoffs: 68% is for ±1 SD, 99.7% for ±3 SD, and 50% does not align with these standard intervals.