The results of a national survey showed that on average, adults sleep 7.1 hours per night. Suppose that the standard deviation is 1.7 hours and that the number of hours of sleep follows a bell-shaped distribution. If needed, round your answers to two decimal digits. If your answer is negative use "minus sign". (a) Use the empirical rule to calculate the percentage of individuals who sleep between 3.7 and 10.5 hours per day. Enter your answer as a percentage. % (b) What is the z-value for an adult who sleeps 8 hours per night? (c) What is the z-value for an adult who sleeps 6 hours per night?

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.)