Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. (2 points) 3, -13, and 5 + 4i f(x) = x4 - 8x3 - 12x2 + 400x - 1599 f(x) = x4 - 200x2 + 800x - 1599 f(x) = x4 - 98x2 + 800x - 1599 f(x) = x4 - 8x3 + 12x2 - 400x + 1599

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?