Problem list
1. A wine importer has the opportunity to purchase a large consignment of 1947 Chateau Lafite Rothschild wine. Because of the age of the wine, some of it may have turned into vinegar. However, the only way to determine whether a bottle is still good is to open it and drink some. As a result, the importer has arranged with the seller to randomly select and open 50 bottles. Suppose the importer believes that 30% of the bottles will be spoiled.
(a) What is the distribution of the sample proportion of spoiled bottles of wine?
(b) Find the probability that the sample proportion of spoiled bottles of wine exceeds 0.40?
(c) Find the probability that the sample proportion of spoiled bottles of wine falls between 0.25 and 0.42?