We saw that, under certain circumstances, the binomial distribution can be approximated by two other distributions that are simpler to work with. In each of the following cases, apply both approximations, if possible, and compare the answers. Indicate which one you think is closer to the correct answer. If an approximation is not possible, indicate why you think so. You may use calculators or MATLAB programs for calculation.:
a) A measuring device makes errors with a probability of 0.001 on each measurement. What is the probability of more than 20 errors in 10,000 measurements?
b) A difficult experiment has a probability 0.8 of succeeding each time it is done. What is the probability of 98 successful experiments in 100 attempts?