The smallest number that can be added to 1 that gives a sum that is different from 1 is called the machine epsilon, εm. Find the machine epsilon and compare it to what you guessed analytically. For n...

The smallest number that can be added to 1 that gives a sum that is different from 1 is called the machine epsilon, εm. Find the machine epsilon and compare it to what you guessed analytically.

For n = 30 and p = 1/2, compute the probability that a binomial random variable is greater than 20 and estimate the accuracy of your answer. Compare it to the normal approximation.