Answer:
85.71% probability that it takes Emma more than 5 minutes to wait for the train
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]
Uniformly distributed between 4 minutes and 11 minutes.
This means that [tex]a = 4, b = 11[/tex].
What is the probability that it takes Emma more than 5 minutes to wait for the train?
Either it takes 5 or less minutes, or it takes more than 5 minutes. The sum of the probabilities of these events is 1. So
[tex]P(X \leq 5) + P(X > 5) = 1[/tex]
We want to find [tex]P(X > 5)[/tex]. So
[tex]P(X > 5) = 1 - P(X \leq 5) = 1 - \frac{5 - 4}{11 - 4} = 0.8571[/tex]
85.71% probability that it takes Emma more than 5 minutes to wait for the train
