Final answer:
About 99.7% of observations lie within ±3 standard deviations from the mean in a normal distribution, according to the Empirical Rule, which applies to symmetric, bell-shaped distributions.
Step-by-step explanation:
The question is about the Empirical Rule and its application in statistics. Specifically, it relates to how much of the data in a normal distribution is contained within certain numbers of standard deviations from the mean.
About 68 percent of observations are covered within ±1 standard deviation, about 95 percent within ±2 standard deviations, and about 99.7 percent are within ±3 standard deviations from the mean.
Therefore, the correct answer to the question, "About what portion of observations is covered by ±3 standard deviations around the mean?" is 99.7%.
The Empirical Rule or the 68-95-99.7 rule is key to understanding data distribution in statistics, particularly for data that follows a bell-shaped, symmetric distribution such as the normal or Gaussian distribution.