You’ll often hear the expression, "this is accurate to plus or minus two standard deviations." assuming that the population (or sample) has a normal distribution, what percentage of the population (or sample) is included in the quantity, "plus or minus two standard deviations"?

Given:
Mean population = 289,294
Standard deviation = 461,176
percentage of the population of all counties is within 1 standard deviation of the mean

Let us follow the 68-95-99.7 rule

For the normal distribution, the values less than one standard deviation away from the mean account for 68% of the set; while two standard deviations from the mean account for 95%; and three standard deviations account for 99.7%.

The percentage of population of all counties within one standard deviation of the mean is 68%