[5 marks] Cars pass UNSW Fitness Centre on High street according to a Poisson process with rate 7 per minute in the morning hours on weekdays. Using RStudio answer the following questions. a) [1 mark] What is the probability that no car passes this location over a 30-second period on Monday morning? (Enter your answer correct to 4 decimal places) b) [2marks] Find the probability that over a 2-minute period, more than 24 cars pass this location on Tuesday morning. (Enter your answer correct to 4 decimal places) c) [2 marks] Assuming that you have observed 5 cars in the first 30 seconds of a given minute, what is the probability that there will be no more than 7 cars passing the Fitness Centre during this minute? (Enter your answer correct to 4 decimal places)