[Inference with Single Proportion, Confidence Intervals] Let researchers want to analyse a certain proportion quantity by using a random sample with n observations. Suppose that the true popula- tion proportion is p = 0.48. (a) Write an expression for the standard error, SE, using the given value for population proportion p (express the answer as function of n). Use this standard error in the following sub-questions of this exercise. (b) Assuming that n is sufficiently large (so we can apply the Central Limit Theorem) write down the asymptotic distribution of the sampling error, pp. (c) Assuming that n is sufficiently large (so we can apply the Central Limit Theorem) find a probability that sample proportion p is not larger than 0.5 (express the answer as a function of n). (d) For n=100, find a probability that the 95% confidence interval is entirely located below 0.5.