4. The survival time (in years) for a patient with lung cancer can be modelled by a random variable X with cumulative distribution function F(:L') = 1 693/5, :1: > 0. (a) Calculate the probability that a patient with lung cancer will survive for more than 3 years. (b) Calculate the median survival time for a patient with lung cancer. (c) In a study of 20 patients with lung cancer, what is the probability that exactly 11 of them will survive for more than 3 years? (d) A larger study collects 100 patients with lung cancer. Calculate a 95% probability interval for the number of these patients who will survive for more than 3 years. [2+2+2+4=10marks]