5. A group of doctors are conducting a clinical trial for an experimental cancer drug. The graph below shows the probability of patient survival as a function of time, t (in months). The functions for Strmted (survival probability of patients treated by the drug) and Spmmbo (survival probability of patients given a placebo) are determined to 15! be: Streged) = e_()2 and Splcaboa) = .9 144 _ (a) (3 marks) Use the given function 15!. Splacabo) = e 144 to calculate the average survival probability of the placebo group for the rst 10 months of the study. Round to 2 decimal places. proba+llty 5: SurvIvJI 1. (b) (3 marks) The efficacy of the drug at any time 1' Z 0 can be defined as 13(7) = f (Sag-gated\") Splacgbo(t)) alt. 0 Note: This can be thought of as representing a difference of areas. Use a Riemann sum with 5 sub-intervals of equal width to approximate EGO). Use right endpoints. Round your nal answer to 2 decimal places (c) (1 mark) A drug is beneficial if Eli?) > 0 (meaning treated subjects have a larger average survival time over the rst 1' months). Is the drug beneficial at 10 months? (A short one-sentence answer is enough.) (d) (1 mark) Is the drug beneficial at 1' = 20? Explain in 1 or 2 sentences