Final answer:
The phrase "fewer than" means "less than", and the probability that fewer than 9 flights are on time is P(x < 9), making Option 1: True. To calculate probabilities in uniformly distributed datasets, divide the desired range by the total range.
Step-by-step explanation:
The phrase "fewer than" indeed means "less than" in a mathematical context, so the student's understanding that the probability that fewer than 9 flights are on time is equal to P(x < 9) is correct, which makes Option 1: True. If we are given the amount of time, in minutes, that a person waits for a bus is uniformly distributed between zero and 15 minutes, the calculation for the probability that a person waits fewer than 12.5 minutes would be:
- Find the total range of time, which is 15 - 0 = 15 minutes.
- Determine the part of the range that is less than 12.5 minutes, which is 12.5 - 0 = 12.5 minutes.
- Divide the part by the whole range to get the probability: 12.5 / 15.
This result means the probability is far more likely than not, that a person will wait fewer than 12.5 minutes for the bus. Other probability problems presented may vary in complexity and require different calculations, including the use of exponential distributions to model behaviors like the number of days ahead travelers purchase their airline tickets, or determining percentiles for a given data set.