In the figure below, triangle O P N is a reflected image of triangle M P N. Anne states that reflections preserve side lengths, so stack P N with bar on top approximately equal to stack P N with bar on top comma space stack P M with bar on top approximately equal to stack P O with bar on top comma and stack M N with bar on top approximately equal to stack O N with bar on top comma therefore the triangles are congruent. Tim states that reflections preserve angle measures, so angle M P N approximately equal to angle O N P comma space angle M N P approximately equal to angle O P N comma and angle P M N approximately equal to angle P O N comma therefore the triangles are congruent.

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?