Final answer:
The given scenarios involve calculating probabilities and interpreting statistics without specific distribution information provided. A variety of statistical tests and probability formulas would be used depending on the scenario, assuming we know the distribution of clearance times, flight delays, parking space availability, and other factors.
Step-by-step explanation:
We have been given several scenarios that revolve around probabilities and statistics related to airports, airplanes, and the services associated with them. To comment on each situation correctly, it's important to recognize that we need additional information about the distributions of the random variables involved, which are not provided in the question. However, general guidance and methodologies can be discussed.
For the question regarding Airport X:
Without information about the distribution of clearance times at Airport X, we cannot calculate the probability P(X<15) directly. If we assume that the clearance times follow a specific distribution, we would use its probability density function to calculate the desired probability.
In regard to the question about Flight Delays:
The traveler seems to be disputing the variance of the flights' delays more than the average because he has calculated a sample standard deviation that suggests the variance might be higher than claimed. If we were to validate the traveler's dispute, we would conduct a chi-square test for variance, with H0: σ² ≤ 150 and an alternative hypothesis accordingly, depending on whether we're using a one-tailed or two-tailed test.
Probability of Parking Space:
If the time to find a parking space follows a normal distribution, we can calculate the probability of finding a parking space in less than a certain amount of time using the z-score formula. Again, the specific probabilities require values from the standard normal distribution.
Sky Train Waiting Times:
For the Sky Train, which has uniform waiting times, the probabilities are based on the characteristics of a uniform distribution. Here, the formulas are straightforward, as the probability is uniform over the range of possible waiting times between trains.
Buying Airline Tickets:
The time ahead that travelers buy tickets, if exponentially distributed, would allow us to calculate probabilities using the exponential distribution's formula. For instance, the probability of purchasing fewer than 10 days in advance or the median waiting time to purchase can be computed accordingly.