A gambler playing roulette decides to make a "section bet" covering the numbers 1-12. This bet pays 2 to 1 and has chance 12/38 = 6/19 of winning on any particular play. The gambler bets 100 times, betting $50 each time.

(a) Write down the box model to represent this situation, including the values on the tickets, the number of repeats of each ticket, and how many draws we will make with replacement from the box.

(b) The average of this box is ___________ and the SD of the box is ____________.

(c) In 100 plays, the gambler's net gain (total amount won or lost) has an expected value of $___________, with a standard error of $___________.

(d) What is the chance that the gambler comes out ahead (has a positive net gain) after the 100 plays? Use the normal approximation to calculate this. ___________%