import random


def pick_member(collection):
    """Applies the Central Limit Theorem to random index picking.

    The CLT states that the normalized sum of independent variables tends
    toward a normal distribution. This function averages three results from a
    uniform random function in the domain [0, 1) and stretches that over the
    length of the given collection to pick a random member. The resulting
    distribution is close to normal, but truncated within the range of the
    collection, without the need for clamping or rejection.

    Why exactly three random picks approximate a normal distribution very well
    but four or more don't (too narrow) is still unclear to me and is left as
    an exercise for a later date. For now we'll call it a success.
    """
    average = sum(random.random() for _n in range(3)) / 3
    return collection[int(average * len(collection))]