Francis is hanging a painting on a wall, he wants the height of the centre of the painting to be located so that no visitors need to look up or down more than 5° to view the centre of the painting when standing 3 m away. If he expects visitors eyes to be between 152 cm to 200 cm off the ground, what is the range of heights that he can hang the centre of the painting, to the nearest centimetre?

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?