Would like to check my homework please.

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. Plpo 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? Circle all that apply, and fill in the blank if you circle statement (5). 121 Exactly 70% of all the wines were ruined. The proportion of all wines ruined is likely to be less than 70%, but will not be more than 70%. Nor 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%. Make sure you are able to support your answer(s) with no more than one sentence. 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