According to the material, which statement describes a property of the normal distribution?

According to the material, which statement describes a property of the normal distribution?

• A. 68% bounded by one standard deviation below the mean and above the mean
• B. 34% is the area within one standard deviation of the mean
• C. 48% bounded by two standard deviations above or below the mean
• D. 95% bounded by three standard deviations above or below the mean

Answer: (A)

The normal distribution follows the empirical rule: most values lie close to the mean, with the spread set by the standard deviation. About 68% of observations fall within one standard deviation of the mean, meaning the interval from mean minus one standard deviation to mean plus one standard deviation contains roughly 68% of the data. This directly matches the described property. The other statements mix up these proportions: within one standard deviation, the total area is not 34% (that 34% represents half the central region on one side of the mean). Two standard deviations contain about 95% of observations, not 48%. And three standard deviations contain about 99.7%, not 95%.

The normal distribution follows the empirical rule: most values lie close to the mean, with the spread set by the standard deviation. About 68% of observations fall within one standard deviation of the mean, meaning the interval from mean minus one standard deviation to mean plus one standard deviation contains roughly 68% of the data. This directly matches the described property.

The other statements mix up these proportions: within one standard deviation, the total area is not 34% (that 34% represents half the central region on one side of the mean). Two standard deviations contain about 95% of observations, not 48%. And three standard deviations contain about 99.7%, not 95%.