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Before starting to play the roulette in a casino you want to look for biases that you can exploit. Youtherefore watch 100 rounds that result in a number between 1 and 36 and you count the number ofrounds for which the result is odd. If the count exceeds 55, you decide that the roulette is not fair.Assuming that the roulette is fair, find an approximation for the probability that you will makethe wrong decision.

Respuesta :

okpalawalter8

Answer:

[tex]P(n>55)=0.1357[/tex]

Step-by-step explanation:

From the question we are told that:

Sample size n=100

Sample space n'=36

Generally the equation for the mean number of times odds appears is mathematically given by

[tex]\=x_o=hp[/tex]

[tex]\=x_o=100*0.5[/tex]

[tex]\=x_o=50[/tex]

Generally the equation for standard deviation is mathematically given by

[tex]\sigma=(hp(1-p))^{1/2}\\\sigma=(50(0.5))^{1/2}[/tex]

[tex]\sigma=5[/tex]

Therefore probability to make wrong decision P(n>55)

[tex]P(n>55)=1-P(z<50.5/5)\\P(n>55)=1-P(z<1.1)\\P(n>55)=1-0.86[/tex]

[tex]P(n>55)=0.1357[/tex]

abiolataiwo2015

An approximation for the probability that you will make the wrong decision is 0.1587.

Probability

S=Number of time that the result was odd

n=100

p=0.5

Hence:

E[S]=100×0.5

E[S]=50

Standard deviation=√100×0.5×0.5

Standard deviation√25

Standard deviation=5

Using normal approximation to the binomial

P(S≥55)=P(S-50/5 ≥ 55-50/5)

P(S≥55)=1-P(z ≤ 1)

P(S≥55)=1-0.8413

P(S≥55)= 0.1587

Inconclusion  an approximation for the probability that you will make the wrong decision is 0.1587.

Learn more about probability here:https://brainly.com/question/24756209

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