How many standard deviations account for 95% of cases in a normal distribution?

How many standard deviations account for 95% of cases in a normal distribution?

• A. One standard deviation
• B. Two standard deviations
• C. Three standard deviations
• D. Four standard deviations

Answer: (B)

In a normal distribution, approximately 95% of the data falls within two standard deviations from the mean. This concept is derived from the empirical rule, also known as the 68-95-99.7 rule, which outlines the percentage of values that lie within one, two, and three standard deviations from the mean in a normal distribution. Specifically, about 68% of data points are found within one standard deviation of the mean, approximately 95% are within two standard deviations, and around 99.7% fall within three standard deviations. Therefore, recognizing that a coverage of 95% correlates directly with two standard deviations confirms that this is indeed the correct representation of the spread of data within a normal distribution.

In a normal distribution, approximately 95% of the data falls within two standard deviations from the mean. This concept is derived from the empirical rule, also known as the 68-95-99.7 rule, which outlines the percentage of values that lie within one, two, and three standard deviations from the mean in a normal distribution.

Specifically, about 68% of data points are found within one standard deviation of the mean, approximately 95% are within two standard deviations, and around 99.7% fall within three standard deviations. Therefore, recognizing that a coverage of 95% correlates directly with two standard deviations confirms that this is indeed the correct representation of the spread of data within a normal distribution.