The wedding date for a couple is quickly approaching, and the wedding planner must provide the caterer an estimate of how many people will attend the reception so that the appropriate quantity of food is prepared for the buffet. The following table contains information on the number of RSVP’ed guests for the 225 invitations. Based on her experience, the wedding planner knows it is extremely rare for guests to attend a wedding if they notified that they will not be attending. Therefore, the wedding planner will assume that no one from these 50 invitations will attend. The wedding planner estimates that the each of the 50 guests planning to come solo has a 75% chance of attending alone, a 20% chance of not attending, and a 5% chance of bringing a companion. For each of the 100 RSVPs who plan to bring a companion, there is a 90% chance that she or he will attend with a companion, a 5% chance of attending solo, and a 5% chance of not attending at all. For the 25 people who have not responded, the wedding planner assumes that there’s an 80% chance that each will not attend. If any of these individuals does attend, there is a 75% chance that she or he will attend alone and a 25% chance that she or he will bring a companion.
Number of Invitations . RSVP’ed Guests
50 ............. 0
50 ............. 1
100 ............. 2
25 ........ No response
a. Assist the wedding planner by constructing a simulation model to determine the expected number of guests who will attend the reception. Base your estimate on 1000 replications of the wedding reception.
b. To be accommodating hosts, the couple has instructed the wedding planner to use the simulation model to determine X, the minimum number of guests for which the caterer should prepare the meal, so that there is at least a 90% chance that the actual attendance is less than or equal to X. Base your estimate on 1000 replications of the wedding reception.