A certain gambler's daily income (in dollars) is a random variable X uniformly distributed over the interval -3 to 3.
(i) Find approximately the probability that after 100 days of independent play he will have won more than 200 dollars.
(ii) Find the quantity A that the probability is greater than 95 % that the gambier'S winnings (which may be negative) in 100 independent days of play will be greater than A.
(iii) Determine the number of days the gambler can play in order to have a probability greater than 95 % that his total winnings on these days will be less than 180 dollars in absolute value.