3. A dartboard is partitioned into 20 wedges of equal size, numbered 1 through 20. Half the wedges are painted red, and the other half are painted black. Suppose 100 darts are thrown at the board, and land at uniformly random locations on it. (a) Let X be the number of darts that fall in wedge i. What are E(X) and var(X)? (b) Using a normal approximation, give an upper bound on X; that holds with 95% confidence.