function normalDistributionRandom(min, max, mean, std_dev) {
    // 参考: https://www.cnblogs.com/zztt/p/4025207.html
    let realMax = max + 1;

    let u = 0.0, v = 0.0, w = 0.0, c = 0.0;
    do {
        u = Math.random() * 2 - 1.0;
        v = Math.random() * 2 - 1.0;
        w = u * u + v * v;
    } while (w == 0.0 || w >= 1.0);
    c = Math.sqrt((-2 * Math.log(w)) / w); // Box-Muller转换

    if (mean === undefined || mean === null) {
        mean = (realMax + min) / 2; // 默认中间
    }
    if (std_dev === undefined || std_dev === null) {
        std_dev = Math.min(Math.abs(realMax - mean), Math.abs(min - mean)) / 3; // 默认三个标准差
    }

    let rand = mean + u * c * std_dev;

    if (rand >= realMax) {
        return normalDistributionRandom(min, max)
    }
    if (rand < min) {
        return normalDistributionRandom(min, max)
    }
    return Math.floor(rand);
}


let count = {};
let start = new Date().getTime();
for (let i = 0; i < 100000; i++) {
    let it = normalDistributionRandom(40, 48, 42);
    count[it + ""] = count[it + ""] || 0
    count[it + ""] += 1;
}
console.log(new Date().getTime() - start + "ms", count);

测试结果，性能够用

19ms {
  '40': 14000,
  '41': 17423,
  '42': 18901,
  '43': 17892,
  '44': 14750,
  '45': 9717,
  '46': 4955,
  '47': 1823,
  '48': 539
}