In a normal distribution, approximately what percentage of observations fall within two standard deviations from the mean?

In a normal distribution, approximately 95% of observations fall within two standard deviations from the mean. This result is derived from the properties of the normal distribution, which is symmetric about the mean and follows a specific empirical rule often referred to as the 68-95-99.7 rule.

According to this rule, about 68% of observations lie within one standard deviation from the mean, approximately 95% fall within two standard deviations, and about 99.7% are within three standard deviations. Thus, the correct response accurately captures the percentage of data points that are within two standard deviations of the mean in a standard normal distribution. This concept is fundamental in statistics as it provides insight into the variability and spread of data about the mean.

Understanding this distribution allows statisticians and data analysts to make inferences and decisions based on the probability of observations falling within certain ranges, which is crucial for hypothesis testing and confidence interval estimation.