Todd is playing a carnival game in which a ball of 1 of 3 colors (red. green, or purple) comes out of the machine whenever he puts money into it. Red balls are worth 1 point; green balls are worth 5 points; purple balls are worth 10
points. He has 5 times as many red balls as green ones, and he has 1 more purple ball than he has green balls.
Currently, he has a total of 150 points. How many purple balls does he have?

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%