一道Princeton的数学标准方差题 请教

The members of the newest recruiting class of a certain military organization are taking their physical conditioning test, and those who score in the bottom 16% will have to retest. If the scores are normally distributed, and have an arithmetic mean of 72, what is the score at or below which the recruits will have to retest?

1) There are 500 recruits in the class

2) 10 recruits scored 82 or higher.

答案是C.

书中的解释（大意）：When combine the 2 statements, we can calculate that those 10 top-scoring recruits make up the top 2% of the class as a whole. And since the mean is 72, and the 2% represents the third standard deviation above the mean（deviation above the mean begins at 82), then there are 2 standard deviations between 72 and 82. Hence the deviation is 5. We now know the entire upper half of the curve: 1st is between 72-77, 2nd is between77-82, and the 3rd runs from 82-87. More important, we now know that one standard deviation equals 5 points, so that bottom 16%--also know as the second and third standard deviation below the mean--are those that score at or below 67.

红色字体就是我不明白的地方，是通过什么方法确定那16%的人是在第2和3的方差内呢？？？之前的解释 都明白就是后面到确认那16%的范围不清楚！！

望各位帮忙帮忙！！！thx

68-95-99.7 rule,

只要记住这两个就好了，mean是72，分数高于82的占2%(10/500),就代表82这个数离mean 72有两个方差standard deviation ，82-72得出方差为10/2=5,那么16%的那些人就是离mean 72一个方差的，也就是72-5=67

可以这样理解吗？

因为高分的人只占2%，没有达到题目中16%的要求，就可以理解为16%的人是由第二个deviation以外的人所占的比例吗？就是由77分以上的人占16% 同理推出16%以下的人是在67分以下这样吗？

ding.我也不懂,求解~