A 1000 gallon tank, initially full of water, develops a leak at the bottom. Given that 200 gallons of water leak out in the first 10 minutes, find the amount of water, A(t), left in the tank t minutes after the leak develops if the water drains off at a rate proportional to the amount of water present. a) A(t) = 1000 (4/5)^-1/10 t b) A(t) = 1000 e^1/10 t c) A(t) = 1000 (2/3)^1/10 t d) A(t) = 1000 (1004/5)^t e) A(t) = 1000 e^-1/10 t f) None of the above.

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?