Calvin works at a pizza place making pizzas. If he is working alone, he can make an average of 15 3/4 per hour. If he works with his friend Megan, he tends to get distracted, and his rate falls by 1/2 per hour. How many pizzas can Calvin make in a 8- hour shift with Megan? Explain the operations that will be needed to solve this problem, ans then solve it.

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?