Ninety-five percent of the parts coming off an assembly line are non-defective what is the probability that of 500 parts fewer than 472 are non-defective?

Homework question? This is actually not a question of probability: if 95% of the parts are non-defective, then 0.95 * 500 = 475 parts are non-defective. So there is zero (0) probability that fewer than 472 parts are non-defective. The question is different when any part has a probability (chance) of 95% of being non-defective. This is a so called Binomial distribution. google knows the answer.