Let the null model be that the true capacity is mu_0=5000 milliampere hours (mAh) and that measurements are Normally distributed around this with standard deviation equal to sigma=500 mAh . Let the actual capacity be mu_1=5300 mAh.

Suppose you make n independent measurements, calculate the Z-statistic, and perform a 1-sided Z-test of the null hypothesis that sample comes from the null model. What is the probability that the p-value for $\bar x$ will satisfy p<=.01 for $n$ in {16,49}?