An SRS of 100 flights by Falcon Airlines shows that 82 were on time. An SRS of 100 flights by WinterSoldier Airlines shows that 68 were on time. Let Pn be the proportion of on-time flights for all Falcon Airline flights, and let Pw be the proportion of all on-time flights for all WinterSoldier flights. A 95% confidence interval for the difference Pn-Pw is:

Afriend of mine is giving a dinner party. his current wine supply includes 10 bottles of zinfandel, 8 of merlot, and 11 of cabernet (he only drinks red wine), all from different wineries. (a) if he wants to serve 3 bottles of zinfandel and serving order is important, how many ways are there to do this? ways (b) if 6 bottles of wine are to be randomly selected from the 29 for serving, how many ways are there to do this? ways (c) if 6 bottles are randomly selected, how many ways are there to obtain two bottles of each variety? ways (d) if 6 bottles are randomly selected, what is the probability that this results in two bottles of each variety being chosen? (round your answer to three decimal places.) (e) if 6 bottles are randomly selected, what is the probability that all of them are the same variety? (round your answer to three decimal places.)