You sit down to buy your first home. Your realtor is excited to sell you a home, the owner is thrilled to have their home sell, and the bank is eager to lend you the money to buy the house. You want to purchase the home for $250,000 and put 20% down. The bank will give you a loan for the remaining $200,000 at a rate of 4.5% APR. While you are ready to move and get settled, you wonder in the back of your mind, “How much is this home really going to cost me?” Neglecting insurance and taxes, how much will you pay for this $250,000 home after you make the last payment on a 30-year mortgage?

Amachine that produces a special type of transistor (a component of computers) has a 2% defective rate. the production is considered a random process where each transistor is independent of the others. (a) what is the probability that the 10th transistor produced is the first with a defect? (b) what is the probability that the machine produces no defective transistors in a batch of 100? (c) on average, how many transistors would you expect to be produced before the first with a defect? what is the standard deviation? (d) another machine that also produces transistors has a 5% defective rate where each transistor is produced independent of the others. on average how many transistors would you expect to be produced with this machine before the first with a defect? what is the standard deviation? (e) based on your answers to parts (c) and (d), how does increasing the probability of an event a↵ect the mean and standard deviation of the wait time until success?