Problem 1: The height of water in a bathtub, w, is a function of time, t. Let P represent this function. Height

is measured in inches and time in minutes.

Match each statement in function notation with a description.

A: P (0)=0

1: After 20 minutes, the bathtub is empty.

B:P (4)= 10

2: The bathtub starts out with no water.

C:P (10) = 4

3: After 10 minutes, the height of the water is 4 inches.

D: P (20) = 0

4: The height of the water is 10 inches after 4 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?