Using Central Limit Theorem to estimate probability Mr. Green bets a dollar on red at roulette 1000 times. Each time, if the player's color comes up, he is paid his stake and gets his original stake back; otherwise he loses his stake. What is the approximate probability that he loses at most 30 dollars? Express your answer in terms of Þ(x) : = px 1 e-t²/2 dt. e √2TT
Using Central Limit Theorem to estimate probability Mr. Green bets a dollar on red at roulette 1000 times. Each time, if the player's color comes up, he is paid his stake and gets his original stake back; otherwise he loses his stake. What is the approximate probability that he loses at most 30 dollars? Express your answer in terms of Þ(x) : = px 1 e-t²/2 dt. e √2TT
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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![**Using Central Limit Theorem to estimate probability**
Mr. Green bets a dollar on red at roulette 1000 times. Each time, if the player's color comes up, he is paid his stake and gets his original stake back; otherwise he loses his stake. What is the approximate probability that he loses at most 30 dollars? Express your answer in terms of
\[
\Phi(x) = \int_{-\infty}^{x} \frac{1}{\sqrt{2\pi}} e^{-t^2/2} dt.
\]
**Explanation:**
The problem involves estimating the probability of Mr. Green losing at most 30 dollars after betting 1000 times, using the properties of the normal distribution. The function \(\Phi(x)\) represents the cumulative distribution function of the standard normal distribution, which is integral to solving this problem with the Central Limit Theorem.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F34c2413e-3f58-45fc-ab9f-9704a2813bd8%2F2428bd27-0298-4d92-b72f-16a9c0ed580c%2Fu4z2zjg_processed.png&w=3840&q=75)
Transcribed Image Text:**Using Central Limit Theorem to estimate probability**
Mr. Green bets a dollar on red at roulette 1000 times. Each time, if the player's color comes up, he is paid his stake and gets his original stake back; otherwise he loses his stake. What is the approximate probability that he loses at most 30 dollars? Express your answer in terms of
\[
\Phi(x) = \int_{-\infty}^{x} \frac{1}{\sqrt{2\pi}} e^{-t^2/2} dt.
\]
**Explanation:**
The problem involves estimating the probability of Mr. Green losing at most 30 dollars after betting 1000 times, using the properties of the normal distribution. The function \(\Phi(x)\) represents the cumulative distribution function of the standard normal distribution, which is integral to solving this problem with the Central Limit Theorem.
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