The probability of winning the top prize on a Plinko board...

The probability of winning the top prize on a Plinko board is 0.24. The game is played 50 times. Assume that the number of times a person can win is normally distributed. (binomial) a) What is the expected mean number of wins? (2 marks) b) What is the expected standard deviation of number of wins? (2 marks) c) What is the probability of winning exactly 15 times? (4 marks)

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. $$\begin{array}{c|ccccc}{x} & {\$ 0} & {\$ 100} & {\$ 500} & {\$ 1000} & {\$ 10,000} \\ \hline p(x) & {.39} & {.03} & {.11} & {.24} & {.23}\end{array}$$ (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.

Probability with Applications in Engineering, Science, and Technology

Discrete Random Variables and Probability Distributions

Expected Value and Standard Deviation

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