Uniform distribution of highway accidents. Accidents occur along a 5-mile stretch of highway at a uniform rate. The following “curve”

depicts the probability density function for accidents along this stretch:

Notice that this “curve” demonstrates the first two basic properties of probability density functions:

• Property 1: The area under the curve between any two points is never less than 0 and is never more than 1. (Probabilities are always between 0 and 1, inclusive.)

• Property 2: The total area under the curve sums exactly to 1.

Respond to each of the following questions using the “area under the curve” principles introduced in the chapter.

(a) What is the probability that an accident occurred in the first mile along this stretch of highway?

(b) What is the probability that the accident did not occur in the first mile?

(c) What is the probability that an accident occurred between miles 2.5 and 4?

(d) What is the probability that an accident occurred either within the first mile or between miles 2.5 and 4?