for a normal distribution, chatgpt suggests the box-muller transform and calling out to awk (which is a scripting language that continues to surprise me; it seems underrated?)

    normal_random() {
        start=$1
        end=$2
        range=$(echo "$end - $start" | bc -l)

        awk -v start=$start -v range=$range -v seed=$RANDOM '
        BEGIN {
            srand(seed);
            u1 = rand();
            u2 = rand();
            z0 = sqrt(-2 * log(u1)) * cos(2 * 3.14159265358979323846 * u2);
            z1 = sqrt(-2 * log(u1)) * sin(2 * 3.14159265358979323846 * u2);

            random_number = start + (z0 * (range / 6)) + (range / 2);
            printf("%.0f\n", random_number);
        }'
    }

In testing it out, they did seem normally-distributed but rerunning it quickly did seem to produce more consecutively duplicate results than would be expected, not sure why that would be (I was using ranges of 0-10 and 0-20, perhaps the probability of normally-distributed consecutive dupes in that range is quite higher?)

EDIT: Nope, there's definitely something wrong with this, possibly the rand() call(s)? Can anyone guess? (A real-world example of the perils of relying on chatGPT!) EDIT2: Figured it out. srand with no args seeds to the current second, making any run of this function within the same second produce the same result. Fixing this left as an exercise to the reader EDIT3: I fixed it by seeding it externally via $RANDOM.