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a simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6, respectively. all 10 dice were rolled, and the average of the 10 numbers appearing faceup was recorded. the process was repeated 20 times. which of the following best describes the distribution being simulated?
a simulation was conducted using 10 fair six-sided dice, where the faces were numbered 1 through 6, respectively. all 10 dice were rolled, and the average of the 10 numbers appearing faceup was recorded. the process was repeated 20 times. which of the following best describes the distribution being simulated?
Final answer:The simulation of rolling 10 fair six-sided dice multiple times and recording averages is best described by a normal distribution, as per the Central Limit Theorem. The random variable in question is the average of the dice rolls.Explanation:The question describes a process of simulating the statistical distribution of averages obtained from rolling 10 fair six-sided dice multiple times. When multiple fair dice are rolled and averages of their outcomes are considered, the distribution being simulated is approximately normal distribution due to the Central Limit Theorem.This theorem states that as the sample size (in this case, the number of dice) increases, the distribution of the sample mean will approach a normal distribution, regardless of the original distribution of the data, provided the samples are all independent and identically distributed.The random variable of this distribution is the average value from rolling the 10 dice. To collect a sample of ten values of this random variable, one would roll the 10 dice, calculate the average, and repeat this process 10 times.The simulated averages can then be analyzed to understand various statistical properties, such as the mean and standard deviation, of the underlying distribution....