During halftime of a soccer game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 4 feet with an initial upward velocity of 72 feet per second. The T-shirt is caught 31 feet above the field. How long will it take the T-shirt to reach its maximum height? What is the maximum height? What is the range that models the height of the T-shirt over time?

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?