An article in the Los Angeles Times (Dec. 3, 1993) reports that 1 in 500 people carry the defective gene that causes inherited colon cancer. In a sample of 2000 individuals, we are interested in the number of individuals who carry this gene. Typically 1 binomial distribution can be used to model this number. However, in the case of large n and small p, we can use Poisson distribution approximately. Answer the following questions using R commands. (a) Use binomial distribution to calculate the the probability that between 5 and 8 (inclusive) carry the gene. (b) Use binomial distribution to calculate the the probability that at least 8 carry the gene. (c) Use Poisson distribution to recalculate the approximated probability for part(a) and make comparison. (d) Use Poisson distribution to recalculate the approximated probability for part(b) and make comparison.