A venture capitalist is funding numerous projects. Most of them turn out to be unsuccessful, but the few that make money are enough to get a good return. Over the last three years 80 projects were funded and only 15 of them succeeded. Let p the probability of success and assume that all projects are ex ante alike, meaning that they have the same probability of success. 1) Find the 95% confidence interval for the parameter p of a Binomial Distribution (2.5% quantile value and 97.51% quantile value are q_{0.025}=-1.96 and q_{0.975}=1.96, respectively). 2) Now find the confidence interval for the case in which 800 projects were funded and 150 of them succeeded. A venture capitalist is funding numerous projects. Most of them turn out to be unsuccessful, but the few that make money are enough to get a good return. Over the last three years 80 projects were funded and only 15 of them succeeded. Let p the probability of success and assume that all projects are ex ante alike, meaning that they have the same probability of success. 1) Find the 95% confidence interval for the parameter p of a Binomial Distribution (2.5% quantile value and 97.51% quantile value are q_{0.025}=-1.96 and q_{0.975}=1.96, respectively). 2) Now find the confidence interval for the case in which 800 projects were funded and 150 of them succeeded