Suppose taxi fares from Logan Airport to downtown Boston is known to be normally distributed and a sample of seven taxi fares produces a mean fare of $16.51 and a 95% confidence interval of [$15.96, $17.04]. Which of the following statements is a valid interpretation of the confidence interval?? a. 95% of all taxi fares are between $14.77 and $16.23.
b. We are 95% confident that a randomly selected taxi fare will be between $14.77 and $16.23.
c. The mean amount of a taxi fare is $15.51, 95% of the time.
d. With 95% confidence, we can report that the average taxi fare between Logan Airport and downtown Boston will fall between $14.77 and $16.23.

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.