The time (in mins) between the arrival of patients to an emergency department of a large hospital follows an exponential distribution. The average time between patient amivals is 12 mins. a) What is the probability that no patient arrives within the next 30 mins? (2 points) b) What is the probability that at least one patient arrives within the next 10 minutes? (2 points) c) What is the probability that one patient arrives between the next 5 to 10 minutes? (2 points) d) What is the length of the interval such that the probability of at least one patient arriving is 0.9 ? (2 points) e) Use Excel to visualize the probability density function for this question. (1 point)