The 68-95-99.7 rule says that we can estimate the percent of a normal distribution that is within 1 standard deviation (1σ) from the mean as 68%, the percent within 2σ as 95%, and within 3σ from the mean as 99.7%. This rule will be useless except for numbers that are 0, 1, 2 or 3σ away from the mean. 36 is 0 away from the mean, and 12 is 24 away from the mean. How many σ is 24, when σ is 8? That's right, 3σ. So now we know we're using the part of the rule with 3σ. That part of the rule says if you go up and down from the mean by 3σ each, then you'll enclose 99.7% of the distribution. But we're only going down, not up, so we only get half of that. Half of 99.7% is ... 49.85%
