You are running an experiment in class where you draw colored marbles out of a bag. There are eight marbles in the bag, you will draw five times, and you will replace the marble each time. How many ways can you draw the marbles out of the bag?

The empirical rule states that approximately 68% of a normal distribution falls within one standard deviation of the mean, or . This means, by symmetry of the distribution, that

Now, since the distribution is symmetric about the mean, you have .

So,



More precisely, this probability is around .