Mariana wants to attend Texas A&M. One year at Texas A&M costs approximately $28,000. She currently has $7,000 in savings. Mariana has received a one-time grant of $1,000 and an annual academic scholarship for $6,000. She plans to enroll in the work study program that will pay $10,000 annually for part-time work. How much will Mariana need to borrow in student loans in order to attend Texas A&M for 4 years?

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?