Final answer:
To find the probability that Iman must wait less than 9 minutes to catch the bus, divide the length of the interval from 0 to 9 minutes by the total time interval of 12 minutes.
Step-by-step explanation:
To find the probability that Iman must wait less than 9 minutes to catch the bus, we need to determine the proportion of the total time interval that represents waiting times less than 9 minutes.
Given that the waiting time is uniformly distributed between 0 and 12 minutes, the total time interval is 12 - 0 = 12 minutes.
The probability that Iman waits less than 9 minutes can be calculated by dividing the length of the interval from 0 to 9 minutes (9 - 0 = 9 minutes) by the total time interval of 12 minutes:
Probability = (Length of Interval from 0 to 9 minutes) / (Total Time Interval)
Probability = 9 / 12 = 0.75