. A detergent company periodically tests its products for variations in the fill weight. To do this, the company uses -charts. Eight samples, each containing six detergent boxes, were selected from different batches. Historical data for fill weight (in ounces) of the eight samples is presented below. Sample Sample Mean Sample Range 1 15.80 0.42 2 16.10 0.38 3 16.02 0.08 4 15.95 0.15 5 16.12 0.42 6 16.18 0.23 7 15.87 0.36 8 16.20 0.40 If A2>for the -chart is 0.483, the upper control limit for the -chart (UCL ) will be: a. less than or equal to 14. b. more than 14 but less than or equal to 16. c. more than 16 but less than or equal to 18. d. more than 18.

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.)