****any four parts..but urgent please quickly it's urgent... .. question)Consider a gas station with only four slots where vehicles can fill regular gasoline, only one of which also offers the option of diesel gasoline (in addition to regular gasoline). We assume that the number of vehicles arriving at the gas station follows a Poisson law with an average rate of 57 vehicles per hour. We also know that 5% of these vehicles use diesel fuel. a) What is the probability of having at least 1 diesel gasoline vehicle within a 5 minute interval? b) What is the probability that no vehicle will arrive in the next minute? c) What is the probability of waiting at least 3 minutes before the next vehicle arrives? d) Knowing that there are currently 4 vehicles at the service station, what is the probability that there is more than one diesel vehicle? e) What is the probability of waiting for the arrival of at least 15 vehicles to obtain a first gasoline-diesel vehicle? f) If the service station makes a profit of $16 for each regular gasoline vehicle and a profit of $17 for each diesel gasoline vehicle, calculate the average profit per hour. h