Haley and Sabrina are both training for a race. Haley runs 4.2 miles each day. Sabrina has been running 2/3 as many miles each day as Haley. Next week, Sabrina is going to increase the miles she runs each day by 25%. Haley and Sabrina both train by running 6 days each week. What is the total number of miles Sabrina will run next week to train for the race?

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?