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GarryVolchara [31]
2 years ago
13

A roulette wheel in a casino has 38 slots. If you bet a dollar on a particular​ number, you'll win ​$30 if the ball ends up in t

hat slot and​ $0 otherwise. Roulette wheels are calibrated so that each outcome is equally likely.
Business
1 answer:
Elan Coil [88]2 years ago
3 0

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>

<em />

<em>b) You decide to play once a minute for a total of 1050 times. Find the mean and standard deviation.</em>

<em />

<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>

<em />

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:

\mu=30*0.0263+0*0.9737=0.789\\\\\sigma=\sqrt{0.0263(30-0.798)^2+0.9737*(0-0.798)^2}=\sqrt{0.0263*852.76+0.9737*0.64}\\\\\sigma=\sqrt{23.05} =4.801

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

\mu_s=\mu=0.789\\\\\sigma_s=\sigma/\sqrt{n}=4.801/\sqrt{1050}=4.801/32.404=0.148

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:

z=(x-\mu_s)/\sigma_s=(1-0.789)/0.148=0.211/0.148=1.426\\\\P(X>1)=P(z>1.426)=0.072

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Answer:

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