Question

Alex is in a hurry to get to work and is rushing to catch the bus. She knows that the bus arrives every six minutes during rush hour, but does not know the exact times the bus is due. She realizes that from the time she arrives at the stop, the amount of time that she will have to wait follows a uniform distribution with a lower bound of 0 minutes and an upper bound of six minutes. What is the probability that she will have to wait more than two minutes g

Answer 1

Answer:

0.6667 or 66.67%

Step-by-step explanation:

Since the waiting time is normally distributed between 0 and 6 minutes, for any time 'x' within the interval, the probability the waiting time is longer than 'x' is given by:

$P(t>x) = 1-\frac{x-0}{6-0}=\frac{6-x}{6}$

For x = 2 minutes:

$P(t>2)=\frac{6-2}{6}\\P(t>2)= 0.6667\ or\ 66.67\%$

The probability that she will have to wait more than two minutes 0.6667 or 66.67%