Question

Empirical rule (statistics)Help please!!!

Answer 1

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
`X` be the random variable denoting vehicle speeds along this highway. We want to find
`P(61<X<79)`. To use the rule, we need to rephrase this probability in terms of the mean and standard deviation.

Notice that
`61=70-9=70-3\cdot3`, and
`79=70+9=70+3\cdot3`. In other words, 61 and 79 both lie exactly 3 standard deviations away from the mean, so
`P(61<X<79)\approx99.7\%`.