Desired accuracy

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Professor Johnson is interested in the probability that a certain typeof randomly generated matrix has a positive determinant. His studentattempts to calculate the probability exactly, but runs into difficultybecause the problem requires her to evaluate an integral in 9 dimensions.Professor Johnson therefore decides to obtain an approximateprobability by simulation, i.e., by randomly generating some matricesand observing the proportion that have positive determinants. His preliminaryinvestigation reveals that the probability is roughly 0.05. Atthis point, Professor Park decides to undertake a more comprehensivesimulation experiment that will, with 0.95-level confidence, correctlydetermine the probability of interest to within ±0.00001. How manyrandom matrices should he generate to achieve the desired accuracy?

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