The characteristic of the population of interest in a survey is = 1/, where is the mean of the population. In an EAS of size n = 105, we obtain ybar = 5.25 and s = 0.37. In what follows, we consider = ybar^(1) as an estimator of . (a) Use a (second-order) Taylor series expansion of around ybar = to obtain an approximate expression for the bias of as an estimator of . (b) Use a (first-order) Taylor series expansion of around ybar = to obtain an approximate expression for the bias of as an estimator of . (c) Assuming that the distribution of approximately follows a normal law for sufficiently large values of n, use the result of (b) to obtain a C.I. of at about 95%. [Ignore the bias of and the finite population correction factor, assuming in the latter case that N is very large.] (d) Find a C.I. of at about 95% by first finding an analogous interval for , then inverting the bounds. Compare with the result obtained in (c).