Question

The waiting time at an elevator is uniformly distributed between 30 and 200 seconds. What is the probability a rider must wait between 1 minute and 1.5 minutes?

Answer 1

Answer:

17.65% probability a rider must wait between 1 minute and 1.5 minutes

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 between c and d is given by the following formula

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

For this problem, we have that:

$a = 30, b = 200, c = 1*60 = 60, d = 1.5*60 = 90$

$P(60 \leq X \leq 90) = \frac{90 - 60}{200 - 30} = 0.1765$

17.65% probability a rider must wait between 1 minute and 1.5 minutes