Days until the data take over

Strategies have true daily edges that are normal with variance $5$. A single day of a strategy is its edge plus independent normal noise of variance $40$. The posterior mean of an edge is a weighted average of the strategy's sample mean and the population mean. What is the smallest whole number of days for which the sample mean gets a weight of at least $\frac{3}{4}$? Give a whole number.

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