Acompany has developed a new ink-jet cartridge for its printer that it believes has a longer life-time on average than the one currently being produced. to investigate its length of life, 225 of the new cartridges were tested by counting the number of high-quality printed pages each was able to produce. the sample mean and standard deviation were determined to be 1511.4 pages and 35.7 pages, respectively. the historical average lifetime for cartridges produced by the current process is 1502.5 pages. write down the symbolic form of the hypotheses.

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.