A charity fundraiser has a Spin the Pointer game that uses a spinner like the one illustrated in the figure below. A donation of $2 is required to play the game. For each $2 donation, a player spins the pointer once and receives the amount of money indicated in the sector where the pointer lands on the wheel. The spinner has an equal probability of landing in each of the 10 sectors. 50 51 S2 SI S8 SO PO) $10 SO S1 SI OSO (a) Let X represent the net contribution to the charity when one person plays the game once. Complete the probability distribution of X by finding Plx=$2), P(X-$1), and P(X=-$8). (b) What is the expected value (mean) of the net contribution to the charity for one play of the game? (c) Based on last year's event, the charity anticipates that the Spin the Pointer game will be played 1,000 times. The mean and standard deviation of the net contribution to the charity in 1,000 plays of the game are $700 and $92.79, respectively. Use the normal distribution to approximate the probability that the charity would obtain a net contribution of at least $500 in 1.000 plays of the game.