Fernando built a robot to filter air and water efficiently. He expects the robot to filter more than 512 liters of air and water while using less than 9 Joules of energy. A represents the number of minutes the robot filters air, and W represents the number if minutes the robot filters water. 21A + 142 > 512 represents the number of minutes the robot filters air and water to filter more than 12liters of air and water. 0.36A + 0.6W < 9 represents the number of minutes the robot filters air and water while using less than 9 Joules of energy. Does the robot meet both of Fernando's expectations by filtering air for 15 minutes and filtering water for 5 minutes?

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?