Problem 5. A political interest group would like to know what fraction pe (0, 1) of the population intends to vote for candidate A in the next election. 1000 randomly chosen individuals are polled. 457 of these indicate that they intend to vote for candidate A. Hence the estimate for p is given by the sample proportion p = 0.457. (i) Find a 95% confidence interval of the type (p - e, p + () for the true fraction p from this data. (ii) Now, suppose the polling company does independent polling every week and publishes 95% confidence intervals for each polling. Let T be the first week that the confidence interval does not contain the real p, i.e., p is outside the interval (p - 6, p + (). Find E(T)