A manager of the fitness center, Dana is constantly trying new initiatives to ke

Question

A manager of the fitness center, Dana is constantly trying new initiatives to keep her clients fit. Recent studies show that using several different 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 on each piece of equipment for a total cardio workout of 45 minutes. If the reliability of the bike is 96%, the treadmill is 95%, and the stair stepper is 92%, what is the probability that a new client can complete his or her workout uninterrupted by faulty equipment? B. Also dana has added another cardio "line: to the one discussed above with the same type of equipment. 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?

Explanation / Answer

a)Here bike,treadmill,stair strepper are in series.

Reliability in series=R1*R2*R3

So probability that a consumer can complete his workout uninterruptedly is 0.96*0.95*0.92=0.83904

which is 83.904%

b)The second line consisits of same three components with reliabilities of 80% each.

These three are in series with each other.

So total reliabilty of second line alone=0.80*0.80*0.80=0.512

If a second line is added as a backup to the first line,then it is in parallel with the first line.

Total reliability of first and second lines in parallel=0.42958848 or 42.958848%

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.