I have the following experiment:

Two balls are let fall from a certain high (could be the same or different)

Then for each of them, I get a random number from 0 to 1 with a uniform distribution and multiply the original height. The result is the height that will bounce back.

The whole process is repeated 10 times and note down the number of ball A ended up higher.

An example:

ball_A_Original_Height = 10
ball_B_Original_Height = 10
wins = 0
repeat 10 times:
    new_ball_A_Height = get_random_number(0,1) * ball_A_Original_Height // 0.81 * 10 = 8.1

    new_ball_B_Height = get_random_number(0,1) * ball_B_Original_Height // 0.57 * 10 = 5.7

    if new_ball_A_Height >= new_ball_B_Height then wins += 1

Then I run a simulation with 5.000.000 times the above test and create a dataset with the number of wins from ball A.

If I use an online probability calculator for a Binomial Distribution like this one stattrek, with probability of success 50%, I get that P(X<=5) = 62.30%

But if I use a probability calculator for a Normal Distribution stattrek-normal with the mean and standard deviation of the dataset I created, the same probability P(X<=5) is far less.

Can someone explain it to me?


1 Answer 1


The binomial score has to deal with the case of exactly equal to 5, the normal approximation assumes a continuous variable, so the probability of equaling exactly 5 is 0.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.