Acommon characterization of obese individuals is that their body mass index is at least 30 [bmi = weight/(height)2, where height is in meters and weight is in kilograms]. an article reported that in a sample of female workers, 265 had bmis of less than 25, 158 had bmis that were at least 25 but less than 30, and 123 had bmis exceeding 30. is there compelling evidence for concluding that more than 20% of the individuals in the sampled population are obese?

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.