4. In the rst two months since a new software package got introduced on the market, 2000 customers have purchased the package. It turns out that 500 of these customers are dissatised with the product. Fifteen individuals are randomly sampled from the 2000 customers and questioned about the package- Let the random variable X be the number of dissatised customers in this sample. {a} What kind of probability distribution does X have? {b} Find the expected number of dissatised customers in the sample. to} Set up the calculations needed to nd P[X 1" 3] exactly (don't work it out). {d} Use the binomial distribution to show that P[X :3 3] is approximately equal to 0.5381