(Sarah’s Wedding) Sarah is planning her wedding. She and her fiance´ have signed a contract with a..

(Sarah’s Wedding) Sarah is planning her marriage. She and her fianceˊ bear authorized a lessen delay a caterer that calls for them to explain the caterer the estimate of visitors that conquer imply the acceptation a week precedently the express result. This “final estimate” conquer detail how ample they bear to pay the caterer; they must pay $60 per visitor that they intrust to. If, for stance, they explain the caterer that they look-for 90 visitors, they must pay $5,400 ( = 90 × $60) level if simply, say, 84 visitors profession up. The lessen calls for a surpassing admonish of $85 per extra visitor for the estimate of visitors further what the stranger intrusts to. Thus, if Sarah and her fianceˊ intrust to 90 visitors but 92 profession up, they must pay $5,570 (the primordial $5,400 plus 2 × $85). The whole Sarah faces is that she quiescent does not distinguish the straight estimate of visitors to look-for. Despite research that friends and parentage members answer to their invitations a month ago, some misgiving remains: Her match may—or may not—bring his new girlfriend; her fianceˊ’s seed-plot roommate may—or may not—be operative to engage a holiday from work; and so forth. Sarah has detaild that the look-fored estimate of visitors (i.e., the balance estimate) is 100, but the express estimate could be anywhere from 84 to 116:

Q = Estimate of visitors that profession up to the marriage

f(Q) = Density operation = Prob{Q visitors profession up}

F(Q) = Distribution operation = Prob{Q or fewer visitors profession up}

L(Q) = Loss operation = Expected estimate of visitors over Q

a. How sundry visitors should Sarah intrust to delay the caterer? [15.2]

b. Suppose Sarah intrusts to 105 visitors. What is Sarah’s look-fored account? [15.2]

c. Suppose that the caterer is conquering to exchange the lessen so that if fewer than the estimate of visitors they intrust to profession up, they conquer get a local restore. In point, they simply bear to pay $45 for each “no-show.” For stance, if they intrust to 90 but simply 84 profession, they conquer bear to pay 84 × $60 = 6 × $45 = $5,310. Now how sundry visitors should she intrust to? [15.4]

d. The caterer offers Sarah another liberty. She could pay $70 per visitor, no stuff how sundry visitors profession up; that is, she wouldn’t bear to intrust to any estimate precedently the marriage. Should Sarah fancy this liberty or the primordial liberty ($60 per intrustted visitor and $85 each visitor further the intrustment)? [15.4]