Read this carefully! Explanation of the Flights Data The data set contains all the 243 United Airlines flights that departed Houston in July 2011. For each flight, we are given the following information: DayofMonth = day of the month DayOfWeek = day of the week of departure starting with Monday (1 = Monday, 2 = Tuesday, ..., 7 = Sunday) FlightNum = number identifying the flight Dest = destination airport code (DEN = Denver, IAD = Washington DC, ORD = Chicago, SFO = San Francisco) Distance = distance of flight, in miles DepDelay = departure delay in minutes (negative value indicates the flight departed earlier than the scheduled time) ArrDelay = arrival delay in minutes (negative value indicates the flight arrived at its destination earlier than the scheduled time) For example, the first flight in the data corresponds to the United Airlines flight # 230 that flew from Houston to Chicago on July 1, 2011, Friday. This flght, covering distance of 925 miles, departed 14 minutes later than the scheduled time and arrived in Chicago 15 minutes later than the scheduled time. As another example, the 3rd flight in the data, UA flight #415 flying to Denver departed on time (DepDelay = 0) and arrived in Denver 11 minutes earlier than the scheduled time (ArrDelay = -11). a) If the destination of a flight is known to be Chicago, what is the probabiltiy that there will be arrival delay of less than 40 mins? b) Find the probability that a flight will arrive on or before scheduled time if the destination of the flight is known to be San Francisco. (Read the description of the ArrDelay variable carefully) c) What is the probability that any randomly selected United flight will have less than 40 mins arrival delay?