Under the right conditions, it is possible, due to surface tension, to have metal objects float on water. consider placing a short length of a small diameter steel (sp. wt.=510 lb/ft3) rod on a surface of water. what is the maximum diameter, dmax⁡, that the rod can have before it will sink? assume that the surface tension forces act vertically upward. note: a standard paper clip has a diameter of 0.036 in. partially unfold a paper clip and see if you can get it to float on water. do the results of this experiment support your analysis?

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?