John Anderson bought a home with a 10.5% adjustable-rate mortgage for 30 years. He paid $9.99 monthly per thousand on his original loan. At the end of 5 years he owes the bank $65,000. Now that interest rates have gone up to 12.5%, the bank will renew the mortgage at this rate or John can pay $65,000. John decides to renew and will now pay $10.68 monthly per thousand on his loan. You can ignore the small amount of principal that has been paid. What is the amount of the old monthly payment? ($649.35 OR $682.50?)

What is the amount of the new monthly payment? ($812.50 OR $694.20?)

What is the percent of increase in his new monthly payment? (6.5% OR 6.9%?)

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?