Use R to Solve the Problem.

Suppose that, on average, 1 person in 1000 makes a numerical error in preparing their income tax return. If 10,000 returns are selected at random, find the probability that 6 or 7 or 8 of them contain a numerical error.

A) (5 Marks) Part 1 (Use R) - Use binomial distribution to find the exact probability. Let X be the number of returns with an error. X ~Bin (n =10000, p = 0.001). Want to find P[6X8].

B) (5 Marks) Part 2 (Use R) - Use Poison distribution to approximate the Binomial probability. Let Y be the Poison distribution with parameter =10. When n is very large, p is very small, and np=100000.001=10. With the aid of computer software, we can see how accurate the approximation is. X ~Bin (n =10000, p = 0.001) can be approximated by Y ~Poisson ( = 10).