Ms. Thompson has 120 same-sized tiles with which to make a rectangular
design on her patio floor. 54 of the tiles
are green; the rest are blue. To keep the
rectangular shape, all rows must have
the same number of tiles. If she wants
each row to have the same number of
blue and green tiles, how many rows will
there be if she wants to use all the tiles
and wants the rows to be as long as
possible?

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?