Ascientist is observing a sample of a radioactive substance. the table below shows the amount of the radioactive substance remaining, in milligrams, with respect to time, in hours, since the scientist began observing the sample. time (hours) 1 2 3 4 5 amount remaining (milligrams) 288 144 72 36 18 the independent variable in the relationship is the and should be placed on the . the dependent variable in the relationship is the and should be placed on the .

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?