Question

The amount of time it takes Emma to wait for the train is continuous and uniformly distributed between 4 minutes and 11 minutes. What is the probability that it takes Emma more than 5 minutes to wait for the train?

Answer 1

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.

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

Uniformly distributed between 4 minutes and 11 minutes.

This means that $a = 4, b = 11$.

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

$P(X \leq 5) + P(X > 5) = 1$

We want to find $P(X > 5)$. So

$P(X > 5) = 1 - P(X \leq 5) = 1 - \frac{5 - 4}{11 - 4} = 0.8571$

85.71% probability that it takes Emma more than 5 minutes to wait for the train