An unnoticed mechanical failure

An unnoticed mechanical failure has caused one-fourth of a machine shop’s production of 10,000 pistol firing pins to be defective. A random sample of 25 firing pins was drawn from the population. a.) Explain why this random variable has a binomial distribution? (2 points) b.) What are the mean and the standard deviation of the random variable? (2 points) c.) Find P(X > 4). Use the binomcdf function on your calculator. (2 points) Is it appropriate to use the normal approximation to the binomial for this problem? Support your answer with numbers and a test. Using the normal approximation with the continuity correction, calculate the probaility that you'll observe more than 4 defective firing pins in the random sample of 25. Indicate the X values and the z scores involved. How does your answer compare with the one you have in part c? How do you account for the difference in parts c and e? And sketch the probability distribution and the area you found using the normal approximation with the continuity correction.