The IT manager of a company hired this technology company to update the software on five systems. What is the probability that after the update, at least two of these systems will still have bugs?$(2$ marks$)$

b$.$ The company offers a guarantee that pays $$200$ if a system still has bugs after the update. If the company updates $100$ systems, find the mean and standard deviation of the amount of money that the company will have to pay as a result of this guarantee.$(2$ marks$)$