A technology company offers an inexpensive method of updating software.

However, the method is not foolproof. The company estimates that after the update, $15$ percent of

the systems will still have bugs.

a$.$ 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$)$