Answer:
The length of the arc is centimeters.
Step-by-step explanation:
The length of an arc () with a given central angle is determined by the following expression:
Where:
- Radius, measured in centimeters.
- Central angle, measured in sexagesimal degrees.
Given that and
, then:
The length of the arc is centimeters.
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
.