Answer:
a) 60% probability that the distance is environment friendly.
b) The mean of the distances between the telephone poles is 52.5 meters.
c) The standard deviation of the distance between the telephone poles is 7.22 meters.
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 lower than x is given by the following formula.
Uniform distribution between 40 and 65 meters.
This means that
a) Any distance between poles greater than 50 meters is considered to be environment friendly. What is the probability that the distance is environment friendly?
This is
We have that
So
60% probability that the distance is environment friendly.
b) Find the mean of the distances between the telephone poles
The mean of the uniform distribution is
So
c) Find the standard deviation of the distance between the telephone poles.
The standard deviation of the uniform distribution is:
So