Forge has four hundred page wine list. Story involves a lawsuit...

Forge has four hundred page wine list. Story involves a lawsuit over one of the most renowned restaurant wine collections in the country

Nearly five years ago, Hurricane Andrew raged through South Florida and knocked the air conditioner that cooled the Forge's huge wine collection.According to the restaurant's owners, Alvin and Shareef Malnik, the wine cellar wasn't properly cooled again for five days while temperatures outside climbed to 90 degrees.For a time, it seemed, the wine was unharmed.But within a few months, the Malniks later said, diners started rejecting virtually every bottle of expensive wine they were served.

The Malniks filed an insurance claim several months after the hurricane with Assicurazioni Generali SpA of Italy, which initially paid $450,000.But when the Malniks sought more from that firm and another insurer, a unit of Transamerica Corp., both companies balked.So the Malniks sued, saying the heat had ruined $3 million worth of wine, including 150-year-old vintages.The lawsuit, filed in Dade County Circuit Court, also sought $2 million for property and business losses.

key evidence was collected. Acting as a witness for the Malniks was British wine master Clive Coates.Mr. Coates sampled 80 bottles, found 56 unacceptable, and concluded that 70 percent of the Forge's collection was ruined.

Tasting on behalf of the insurers was another British wine master, Derek Norman Smedley.For his part, Mr. Smedley wasn't much help to the insurers.He tasted several bottles, many from the same vintages and wineries as Mr. Coates's sample, and concluded that about 50 percent tasted as if they had been damaged by heat.

There were some disagreements between the two of them.In the end, Mr. Smedley was able to do for the insurers was to say that he couldn't call the collection "a total write-off." So the case was settled without trial, and the insurers paid $2.75 million to cover wine and other losses.

a) Suppose for the moment that it is known that 65 percent of all the wines in the Forge's collection were ruined, and suppose 16 bottles are chosen at random.

i) What is the expected number (average) of bottles that were ruined?

ii) What is the probability that the first bottle was ruined?

iii) What is the probability that exactly 11 of the bottles were ruined?

iv) What is the probability that at least 10 of the bottles were ruined?

b) Now using Mr. Coates' results, obtain a 95 percent confidence interval for the proportion of the Forge's collection that was ruined.

c) If you were a lawyer for the defense in this suit, you would surely make the point that the 70% figure Mr. Coates had arrived at was merely for the sample of wines he tasted, and ask him if he could be sure that exactly 70% of all the wines in the Forge's collection were ruined.Answering honestly, which of the following statements would Mr. Coates be able to make?this is a multiple choice question. If I pick choice 5 i am not sure how many all wines will be ruined. But i am thinking it might be number 2.

1. Exactly 70% ofallthe wines were ruined.
2. The proportion ofallwines ruined is likely to be less than 70%, but will not be more than 70%.

(3) The exact proportion of all wines ruined is unknown.

(4) The proportion of all wines ruined is likely to be different from 70%.

(5) The exact proportion of all wines ruined is known to be (Fill in the blank)

(6) The proportion of all wines ruined is likely to be more than 70%, but will not be less than 70%.

d) Suppose you wish to obtain a 95% confidence interval for the proportion of wine that was ruined, and you want the confidence interval to be no larger than plus or minus 0.05.You are willing to assume that this proportion is no less than 0.6 (but you want a more refined estimate).How large a sample should you take?