One section of the island-to be sampled by researchers to develop a census of tortoises-is a large square, with a side length of 1 kilometer. researchers intend to place infrared cameras throughout, including along the diagonal of the square. what is the length of the diagonal of this square, expressed in kilometers (rounded to the nearest tenth of a kilometer)? place the length of the diagonal on the number line below. formula used:

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?