Two random variables are such that A has a mean of 80 and standard deviation of 12, while B has a mean of 140 and a standard deviation of 18. Both are roughly normal, and they ARE independent. Show your work for the following, answer the questions below, and submit your work at the end. a) Define D to be the difference: D= B - A. Find the mean of D. b) Find the standard deviation of D. Finally, c) If we randomly chose an A and B value, then what is the probability that D is less than 30?

I'm being volume of cylinder with 13 in. radius and 30 in height answer choices in pic

The function show two sisters' savings account and the rate at which they plan to deposit money

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?