As manager of The Fitness Center, Dana is constantly try-ing new initiatives to keep her clients fit. Recent studies show that using several different cardio regimens for shortperiods of time is more effective than an extended periodof time on one type of equipment. Dana has taken some ofthe existing cardio equipment and arranged them in a lineas follows: stationary bike, treadmill, stair stepper. Clients would select this part of the gym for cardio “circuit train-ing,” 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 thata client can complete his or her workout uninterruptedby faulty equipment?b. Dana has added a second cardio “line” for circuittraining with the same type of equipment as the firstline. This equipment, however, is older with reliabilitiesof 80% each. If only one client were using the cardiocircuit training section of the gym, the second linecould be used as a backup for faulty equipment. Whatis the revised probability of completing a workoutuninterrupted?
As manager of The Fitness Center, Dana is constantly try-
ing 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 train-
ing,” 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?
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