Question

In Grafton, a rural area in Vermont, the distance (in meters) between telephone poles has a uniform distribution between 39 and 67 meters. Suppose two consecutive telephone poles are selected at random. Any distance between poles greater than 54 meters is considered to be environment friendly. What is the probability that the distance is environment friendly?

Answer 1

Answer:

46.43% probability that the distance is environment friendly.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X greater than x is given by the following formula.

$P(X > x) = \frac{b - x}{b-a}$

Uniform distribution between 39 and 67 meters:

This means that $a = 39, b = 67$

Any distance between poles greater than 54 meters is considered to be environment friendly. What is the probability that the distance is environment friendly?

$P(X > x) = \frac{b - x}{b-a}$

$P(X > 54) = \frac{67 - 54}{67 - 39}$

$P(X > 54) = 0.4643$

46.43% probability that the distance is environment friendly.