Professor Johnson is interested in the probability that a certain type of randomly generated matrix has a positive determinant. His student attempts to calculate the probability exactly, but runs into difficulty because the problem requires her to evaluate an integral in 9 dimen- sions. Professor Johnson therefore decides to obtain an approximate probability by simulation, i.e., by randomly generating some matrices and observing the proportion that have positive determinants. His pre- liminary investigation reveals that the probability is roughly 0.05. At this point, Professor Park decides to undertake a more comprehensive simulation experiment that will, with 0.95-level confidence, correctly determine the probability of interest to within ±0.00001. How many random matrices should he generate to achieve the desired accuracy?
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