(a) Waiting at the airport for the plane to take-off is quite boring. Investigate how the departure delays of the flights from New York is distributed by plotting the histogram. Describe the shape of the distribution. Are they doing a good job of keeping the flights on time? Briefly explain your answer. [4 marks] (b) The histogram is very useful to tell us about the distribution, but taking a look at the numerical summary values is also super helpful. Given the shape of the histogram you obtained in the previous question, what would you expect the mean departure delay to compare with the median departure delay? Compute both the mean and the median. Are the results compatible with what you expected? Briefly explain. [3 marks] (c) Similarly, obtain the IQR and standard deviation of departure delay. Is it what you expect? [2 marks (d) Quantiles can be a weird concept to grasp in a theoretical lecture, but they are incredibly useful in practice. [4 marks] i. obtain the 25%, 50%, and 95.149% quantiles and interpret the results. ii. if you were to catch a flight departing New York in 2013, what would be the probability that your flight wouldn't be more than 90 minutes late? (e) What part of the day (i.c., morning, afternoon, or night) is the worst time concerning departure delays to take a flight? To answer this question, create an appropriate plot that displays the distribution of departure delays in each period of the day. What do you observe? (Optional: can you think of a potential reason for these results?) [3 marks]