(a) Recall when finding a confidence interval for t,hc median Of a population, we interval such P (X(a) < 0.5 < X(b)) - and find a and b by plugging in probabilit,y p < 0.5, < Show t,hat, (Iliti[: least, a Of [lie observations fall less t,h.lli 0.5; and ill, b I Of Lhe olmervutions fall less 0.5.) Deliot,e t,he, percentile, Of population, generalize, Lhe confidence interval for tnediutl in class Lest,ing 111 > The confidence interval is sl,ill of Ilie form X(N) < 0.5 < X(b), where 1,1ie values a and b are chosen so l,hnt p (xtaj < X(b)) 10, Derive, the probability P (X(a) < Op < X(b)) by replacing Ille, ().5 in the binomial in class by a general p, and state, how choose a and b. Also, t,he, critical values in nortnal approxilnai,ioll in large-satnple cases.