. You are choosing between two different cheese wedges at the grocery store. Assume both wedges are triangular prisms with bases that are isosceles triangles. The first wedge has a base
that is 2.5 in. wide and a height of 4.5 in., with the entire wedge being 3 in thick. The second
wedge has a base that is 3 in, wide and a height of 4 in., with the entire wedge being 3.5 in.
thick. Which wedge has a greater volume of cheese, and by how much?
The first wedge by 6.375 cubic inches
The first wedge by 12.75 cubic inches
The second wedge by 8.25 cubic inches
The second wedge by 4.125 cubic inches

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?