Question

If a real-valued attribute is normally distributed, we know that approximately 95% of all attribute values lie within

a) one standard deviation of the mean
b) two standard deviations of the mean
c) three standard deviations of the mean
d) four standard deviations of the mean

Answer 1

Approximately 95% of all attribute values in a normally distributed dataset lie within two standard deviations of the mean, as per the Empirical Rule.

Step-by-step explanation:

If a real-valued attribute is normally distributed, approximately 95% of all attribute values lie within two standard deviations of the mean. This is based on the Empirical Rule, which states that for a perfectly bell-shaped, symmetric distribution (also known as the Normal or Gaussian distribution), about 68% of the data lies within one standard deviation, about 95% lies within two standard deviations, and more than 99% lies within three standard deviations of the mean. This rule assumes the distribution is normal and does not generally apply to skewed or non-normal distributions.