Sleeping outlier: A simple random sample of nine college freshmen were asked how many hours of sleep they typically got per night. The results were 8.5 24 9 8.5 8 6.5 6 7.5 9.5

Notice that one joker said that he sleeps 24 a day.

(a) The data contain an outlier that is clearly a mistake. Eliminate the outlier, then construct a 99.9% confidence interval for the mean amount of sleep from the remaining values. Round the answers to at least two decimal places.

(b) Leave the outlier in and construct the 99.9% confidence interval. Round the answers to at least two decimal places.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.