Question: 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 145 invitations. Unfortunately, the number of guests does not always correspond to the number of RSVP'ed guests. Based on her experience, the wedding planner knows it is extremely rare for guests to attend a wedding if they affirmed 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 25 guests planning to come solo has a 75 percentchance of attending alone, a 20 percent chance of not attending, and a 5 percent chance of bringing a companion. For each of the 60 RSVPs who plan to bring a companion, there is a 90 percent chance that she or he will attend with a companion, a 5 percent chance of attending solo, and a 5 percent chance of not attending at all. For the 10 people who have not responded, the wedding planner assumes that there is an 80 percent chance that each will not attend, a 15 percent chance they will attend alone, and a 5 percent chance they will attend with a companion.
RSVP'ed Guest Number of Invitations
0 50
1 25
2 60
No response 10
a. Assist the wedding planner by constructing a spreadsheet simulation model to determine the expected number of guests who will attend the reception.
b. To be accommodating hosts, the couple has instructed the wedding planner to use the Monte Carlo 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 percent chance that the actual attendance is less than or equal to X. What is the best estimate for the value of X?