The table shows Mr. Winkler’s schedule for paying off his credit card balance. A 5-column table with 4 rows. Column 1 is labeled Balance with entries 650 dollars, 556 dollars and 60 cents, 462 dollars and 8 cents, 366 dollars and 42 cents. Column 2 is labeled payment with entries 100 dollars, 100 dollars, 100 dollars, 100 dollars. Column 3 is labeled new balance with entries 550 dollars, 456 dollars and 60 cents, 362 dollars and 8 cents, 266 dollars and 42 cents. Column 4 is labeled rate with entries 0.012, 0.012, 0.012, 0.012. Column 5 is labeled interest with entries 6 dollars and 60 cents, 5 dollars and 48 cents, 4. dollars and 34 cents, 3 dollars and 20 cents. If he continues to make monthly payments of $100, and makes no new purchases, how many more payments will he have to make before the balance is zero?

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?