The mean population of the counties in Florida is 289,294 and the standard deviation is 461,176. It can be assumed that the population is approximately normally distributed. What percentage of the population of all counties is within one standard deviation of the mean?

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24-03-2017
Mathematics

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The mean population of the counties in Florida is 289,294 and the standard deviation is 461,176. It can be assumed that the population is approximately normally distributed. What percentage of the population of all counties is within one standard deviation of the mean?

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taskmasters taskmasters · Answer 1 · 2017-04-07T21:11:13+02:00

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%