A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $20 and then an additional 6 cents per minute of use. In Plan B, the customer pays a monthly fee of $31.50 and then an additional 4 cents per minute of use. For what amounts of monthly phone use will Plan A cost less than Plan B? Use m for the number of minutes of phone use, and solve your inequality for m.

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?