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Identify the parameters [tex]\( p \)[/tex] and [tex]\( n \)[/tex] in the following binomial distribution scenario:
The probability of winning an arcade game is 0.718 and the probability of losing is 0.282. If you play the arcade game 20 times, we want to know the probability of winning more than 15 times. (Consider winning as a success in the binomial distribution.)
To identify the correct parameters [tex]\( p \)[/tex] and [tex]\( n \)[/tex] for this binomial distribution scenario, let's break down the information provided:
1. Probability of Winning (Success): The probability of winning an arcade game is given as 0.718.
2. Number of Trials (Games Played): It is stated that you play the arcade game 20 times. This means the number of trials is 20.
In a binomial distribution scenario: - [tex]\( p \)[/tex] represents the probability of success in a single trial. - [tex]\( n \)[/tex] represents the number of independent trials.
Given this information: - The probability of success, [tex]\( p \)[/tex], is 0.718. - The number of trials, [tex]\( n \)[/tex], is 20.
Thus, the parameters for this binomial distribution are: - [tex]\( p = 0.718 \)[/tex] - [tex]\( n = 20 \)[/tex]
Therefore, the correct answer is: [tex]\[ p = 0.718, n = 20 \][/tex]
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