Using the uniform distribution, it is found that there is a 0.3 = 30% probability that Samantha has to wait less than 4.5 minutes to catch the bus.
It is a distribution with two bounds, a and b, in which each outcome is equally as likely.
The probability of finding a value of at lower than x is:
[tex]P(X < x) = \frac{x - a}{b - a}[/tex]
In this problem, the time is uniformly distributed between 0 and 15 minutes, hence the bounds are a = 0 and b = 15.
The probability that Samantha has to wait less than 4.5 minutes to catch the bus is given by:
[tex]P(X < 4.5) = \frac{4.5 - 0}{15 - 0} = 0.3[/tex]
More can be learned about the uniform distribution at https://brainly.com/question/13889040
