In the popular game Plinko on The Price Is Right, contestants drop a circular disk (a “chip”) down a pegged board; the chip bounces down the board and lands in a slot corresponding to one of five dollar mounts. The random variable X = winnings from one chip dropped from the middle slot has roughly the following distribution.

a. Graph the probability mass function of X.
b. What is the probability a contestant makes money on a chip?
c. What is the probability a contestant makes at least $1000 on a chip?
d. Determine the expected winnings. Interpret this number.
e. Determine the corresponding standard deviation.

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$0 $100 $500 $1000 $10,000 p(x) 0.39 0.03 0.11 0.24 0.23