Pleаse nоte thаt this questiоn cоnsists of five pаrts. You may use MINITAB to find a final answer. However you MUST show all the mathematical work to get to the final answer. Just giving the answer without adequate work/explanation may result in zero for the question. A physician found that for a certain disease a new drug cures 40% of patients. He administers this drug to 10 randomly selected patients with that particular disease. The result of one patient is independent of that for another patient. Let X be the number of patients who are cured by this drug among these 10 patients. 1. What is the distribution of X? Clearly state the name and the values of the parameters of the distribution. 2. Write down the probability mass function f(x) of random variable X define above, and clearly state for which values of X. 3. What is the probability that none among the 10 patients are cured by the drug? Show how you find it. 4. What is the probability that at least one patient is cured by the drug? Show how you find it. 5. Would it be unusual if all ten patients are cured by the drug? In addition to stating whether it would be unusual or not, show the calculations for the relevant probability and explain your conclusion. Use 5% as the cut-off to make your decision.