Repeat trials times: draw n values from $\mathcal{N}(0,1)$, build the interval $\bar{x} \pm 1.96\,\sigma/\sqrt{n}$ using the known $\sigma = 1$, and check whether it contains the true mean of 0. Return the fraction that did.

This is what "95% confidence" actually means: a statement about how often the procedure captures the parameter, not about any single interval.

Seed np.random.seed(seed) inside solve, immediately before drawing.

Input

n = 30
trials = 2000
seed = 0

Output

0.947