As manager of The Fitness Center, Dana is constantly trying new initiatives to keep her clients fit. Recent studies show that using several different cardio regimens for short periods of time is more effective than an extended period of time on one type of equipment. Dana has taken some of the existing cardio equipment and arranged them in a line as follows: stationary bike, treadmill, stair stepper. Clients would select this part of the gym for cardio “circuit training,” spending 15 minutes at each piece of equipment for a total cardio workout time of 45 minutes.
a. If the reliability of the bike is 96%, the treadmill is 95%, and the stair stepper is 92%, what is the probability that a client can complete his or her workout uninterrupted by faulty equipment?
b. Dana has added a second cardio “line” for circuit training with the same type of equipment as the first line. This equipment, however, is older with reliabilities of 80% each. If only one client were using the cardio circuit training section of the gym the second line could be used as a backup for faulty equipment. What is the revised probability of completing a workout uninterrupted?