Miss White is planning her wedding. She has already picked out a cake design that
she likes. The cake is composed of three
tiers. Each tier is either a rectangular
prism. The bottom tier has a length of 20
inches. The second tier has a length of 14
inches and the top tier has a length of 8
inches. Each tier has a height of 6 inches.
The surface of the entire cake will need to
be covered in frosting. See the bottom of
the assignment for a hint if you are
struggling to visualize the cake!
Answer the following questions + show your
work:

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?