Manny is completing a payroll register for his business. One employee, Tomas Nigeria, is single with 4 allowances. Tomas’s hourly rate is $13.45, and he earns time and one-half for overtime. This week, Tomas worked 40 hours of straight time and 7 overtime hours. Tomas has $87.25 withheld for medical insurance which is not taxed. According to the tax table, he should pay $25 in federal taxes. After 6.2% in Social Security and 1.45% in Medicare are withheld, what is Tomas’s net pay?

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?