The National Assessment of Educational Progress (NAEP) includes a mathematics test for eighth-graders. Scores on the test range from 0 to 500. Suppose that you give the NAEP test to an SRS of 1225 eighth-graders from a large population in which the scores have mean = 281 and standard deviation = 127. The mean x will vary if you take repeated samples. The sampling distribution of x is approximately Normal. It has mean = 281. What is its standard deviation? (Round your answer to three decimal places.)

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.)