The normal (Gaussian) distribution: density, cumulative probability and quantiles at any μ and σ, with a curve drawn on canvas so you can see exactly which area the CDF is reporting.
The CDF is the complementary error function evaluated by power series and continued fraction to double precision (not the 1e-7 rational fits from Abramowitz & Stegun), and the quantile function is Acklam's approximation polished by one Halley step — accurate to the last displayed digit.
Frequently asked questions
How do I read a z-score from this?
Set μ = 0 and σ = 1: the CDF at your value is Φ(z), and the two-sided tail P(|Z| > z) is 1 − Φ(z) + Φ(−z). The 68/95/99.7 rule falls out of the same function.
Why not just use a statistics table?
Tables round to four decimals and cover a grid of z values; the exact functions here give every digit at every point, and tie directly into the confidence-interval and hypothesis-testing tools.
中文说明
正态（高斯）分布：任意 μ、σ 下的密度、累积概率与分位数，并在 Canvas 上画出曲线，让 CDF 报告的面积一目了然。
CDF 用幂级数与连分式求补误差函数，精确到双精度（而非 Abramowitz & Stegun 的 1e-7 有理近似）；分位数函数用 Acklam 近似加一步 Halley 抛光——精确到最后一位显示数字。
常见问题
怎么用这个读 z 分数？
把 μ 设 0、σ 设 1：你输入值处的 CDF 就是 Φ(z)，双侧尾部 P(|Z| > z) = 1 − Φ(z) + Φ(−z)。68/95/99.7 法则也是同一函数算出来的。
为什么不直接查表？
表只到四位小数、且只有网格上的 z 值；这里的精确函数在任意点给出全部位数，并直接衔接置信区间与假设检验工具。