In a bell-shaped curve, what percentage of observations fall within one standard deviation of the mean according to the empirical rule?

In a bell-shaped curve, what percentage of observations fall within one standard deviation of the mean according to the empirical rule?

• A. 65%
• B. 68%
• C. 75%
• D. 95%

Answer: (B)

In a normal (bell-shaped) distribution, the empirical rule says about 68% of observations fall within one standard deviation of the mean. This comes from roughly 34% lying between the mean and one standard deviation above, and 34% between the mean and one standard deviation below, adding up to about 68%. If you want the precise figure for the standard normal distribution, it’s 68.27%, but the commonly used rule of thumb is 68%. The remaining observations lie in the tails beyond one standard deviation, about 16% in each tail.

In a normal (bell-shaped) distribution, the empirical rule says about 68% of observations fall within one standard deviation of the mean. This comes from roughly 34% lying between the mean and one standard deviation above, and 34% between the mean and one standard deviation below, adding up to about 68%. If you want the precise figure for the standard normal distribution, it’s 68.27%, but the commonly used rule of thumb is 68%. The remaining observations lie in the tails beyond one standard deviation, about 16% in each tail.