Answer:
a) X=0 P(0)=0.9737
X=30 P(30)=0.0263
b) Mean: 0.789
SD: 4.801
c) P(X>1)=0.072
Explanation:
<em>The question is incomplete:</em>
<em>a) Let denote X your winnings when you play once. State the probability distribution of X.</em>
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<em>b) You decide to play once a minute for a total of 1050 times. Find the mean and standard deviation.</em>
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<em>c) Refer to (b). Using the Central Limit Theorem, find the probability that with this amount of roulette playing, your mean winnings is at least $1 (so, you don't lose money).</em>
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a) X has only two possible states: "0" and "30". The probability distribution for x is:
X=0 P(0)=37/38=0.9737
X=30 P(30)=1/38=0.0263
b) First, we calculate the mean and standard deviation of the population as:

Then, the sampling distribution has these mean and standard deviation:

c) If we use the CLT, we can approximate this binomial distribution with a normal distribution to facilitate the calculations.
To calculate the probabilities of a outcome that is equal or bigger than $1, we first calculate the z-value:
