Roofing contractor offers an inexpensive method of fixing leaky roofs. However, this method is not foolproof. The contractor estimates that after the job is done, 10 percent of the roofs will still leak.
a. The resident manager of an apartment complex hired this contractor to fix the roof of six buildings. What is the probability that after the work has been done, at least two of these roofs will still leak?
b. The contractor offers a guarantee that pays $100 if a roof still leaks after he has worked on it. If he works on 81 roofs, find the mean and standard deviation of the amount of money that he will have to pay as a result of this guarantee.