Please, not just the same answer from chegg copy-pasted (it looks incorrect) Chr
ID: 350080 • Letter: P
Question
Please, not just the same answer from chegg copy-pasted (it looks incorrect)
Christine and Tim are planning for a wedding reception at Logan Ridge, an upstate winery overlooking one of the Finger Lakes. Since the invited guests have not replied on time, they are uncertain about the actual number of guests that will be attending the reception. To the best of the couple's knowledge, the number of guests will be normally distributed with the mean 170 and the standard deviation 20. A manager at Logan Ridge requests the couple for an estimate for the number of guests in order to prepare food. He guarantees that he will prepare food for 10 servings more than the estimate, and will charge based on the higher of the estimate and the actual number of guests. In an unfortunate case that a guest cannot be served, the goodwill cost will be 10 times the per-person charge. Christine and Tim need to provide an estimate for the manager at Logan Ridge (a) Write down an appropriate objective function for the decision that Christine and Tim need to make. (b) What is the optimal solution? Use Excel if necessary.Explanation / Answer
Ans:- We know that in a normal distribution,
the 99% confidence interval for X is Mean-2.58*SD to Mean+2.58*SD.
Where, SD = Standard deviation
For 99% confidence interval, number of guests would range between 170-2.58*20 =118.4 and 170+2.58*20 = 221.6
So number of guests would range between 119 to 222.
So Christine and Tim should provide an estimate of 212 guests because manager can prepare food for 10 serving more than estimate.