Acandy store makes a hard candy mix using a specific ratio of peppermint hard candy, which costs $4.40 per pound, and cinnamon hard candy, which costs $5.40 per pound. overall, the mix ends up costing $5.10 per pound. if the candy store has 210 pounds of peppermint hard candy, how many pounds of cinnamon hard candy will be needed to make the mix?

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?