6. The US Food and Drug Administration wants to estimate the proportion of the US population having diabetes with a 99% condence interval. They want the width of the condence interval (the difference between the right endpoint and the left endpoint] to be no more than 0.04. Determine the necessary sample size in order to achieve this objective. Assume that they have no initial information for the true population proportion prior to the study. 7. In a casino there is a roulette wheel with 18 black slots, 18 red slots, and 2 slots without color (these are called zero and double zero). If a player puts k dollars on red, and the ball stops in one of the red slots, then the player receives back the k dollars she put on the table, plus an additional k dollars (so, in effect, she wins k dollars). If the ball stops in a black slot or in a slot without color, then she loses the k dollars she placed on the table. Player A follows a doubling strategy: rst she bets $1 on red, if she loses she bets $2 on red, if she loses again she bets $4 on red, etc. She quits the first time the ball stops in a red slot, or when she loses all her money, whichever happens rst. Initially she has 63 dollars. Calculate the expected loss of player A