Question

For a normal curve, what percentage of values falls beyond two standard deviations from the mean?

A. 5.55%
B. 4.55%
C. 10.55%
D. 12.55%
E. 13.11%

Answer 1

For a normal curve, approximately 5% of values falls beyond two standard deviations from the mean, with 2.5% in each tail of the distribution.

Step-by-step explanation:

The question pertains to the percentage of data points that fall beyond two standard deviations from the mean on a normal curve. According to the Empirical Rule for a bell-shaped distribution, approximately 95 percent of the data is within two standard deviations of the mean. Since the total area under the curve is 100 percent, the amount outside two standard deviations would be 100% - 95%, which equals 5%. However, because the curve is symmetric, this percentage is split equally between the two tails (upper and lower) of the distribution. Hence, the percentage of values that falls beyond two standard deviations from the mean on either side is 2.5%. Therefore, the total percentage of values beyond two standard deviations from the mean on both sides of the distribution is 5% (2.5% on each side).