Every evening, Sarah walks from her workplace to the nearest train station. The time 7 (in minutes) that Sarah waits for her train to arrive can be modeled using an exponential distribution with rate parameter λ=0.2. The probability density function is given by: (a) f(t) = 0.2 exp(-0.2t), t > 0: What is the probability that Sarah will wait for more than 4 minutes? What is the probability that Sarah will wait for more than 8 minutes, given that she has already waited for more than 4 minutes? (b) Over a period of 10 days, Sarah recorded her train waiting times. What is the probability that on exactly 7 days, Sarah waited for more than 4 minutes? To solve this, construct a binomial model and use the probability from part (a), rounded to the nearest tenth. (c) Use the central limit theorem to approximate the probability that the mean waiting time over 30 days is between 5 and 7 minutes. To do this, find the mean and standard deviation of the sample mean, then use the standard normal distribution to approximate the probability.