The properties of congruence generally match those of equality;
A ≅ A . . . . reflexive property
A ≅ B, B ≅ C ⇒ A ≅ C . . . . transitive property
A ≅ B, A ≅ C ⇒ B ≅ C . . . . substitution
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In this proof, the conclusions (statements 5 and 6) are based on <em>substitution</em>. In each case, the elements of the congruence have previously been shown to be congruent to the same thing. This is the setup for making use of the substitution property of congruence.
The empirical rule you're referring to is the 68-95-99.7 rule, which asserts that for a normal (bell-shaped) distribution, approximately 68% of the distribution lies within 1 standard deviation of the mean; 95% lies within 2 standard deviations of the mean; and 99.7% lies within 3 standard deviations of the mean.
Let be the random variable denoting vehicle speeds along this highway. We want to find . To use the rule, we need to rephrase this probability in terms of the mean and standard deviation.
Notice that , and . In other words, 61 and 79 both lie exactly 3 standard deviations away from the mean, so .