Confidence Interval for a Mean

For a large sample, a $(1-\alpha)$ confidence interval for the mean is $\bar x \pm z\,\frac{s}{\sqrt n}$ with sample std $s$ (ddof=1).

Implement:

• normal_quantile(p): the standard normal quantile, found by bisection on the CDF $\Phi(x) = \tfrac12(1 + \text{erf}(x/\sqrt2))$ over $[-10, 10]$ to within 1e-12
• mean_ci(x, conf=0.95): returns (low, high) using $z =$ normal_quantile(1 - (1 - conf) / 2)