Answer:
37.5% probability that a randomly selected oil change takes at most 20 minutes to complete.
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.
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
For this problem, we have that:
Uniformly distributed between 14 minutes and 30 minutes, which means that [tex]a = 14, b = 30[/tex]
What is the probability that a randomly selected oil change takes at most 20 minutes to complete?
This is [tex]P(X \leq 20)[/tex]. So
[tex]P(X \leq x) = \frac{x - a}{b-a}[/tex]
[tex]P(X \leq 20) = \frac{20 - 14}{30 - 14} = 0.375[/tex]
There is a 37.5% probability that a randomly selected oil change takes at most 20 minutes to complete.
