Two technicians (working separately) are responsible for the repair of 16 cellul
ID: 375996 • Letter: T
Question
Two technicians (working separately) are responsible for the repair of 16 cellular phone towers whenever the towers fail to work. On average, it takes a ½ day for a technician to repair a tower. When a tower breaks down, if both technicians are busy then the first technician to become available will repair the tower. Each tower requires repair approximately once every six days. In order to provide sufficient customer service, at least 13 towers must be in running order. The probability that at least 13 towers will be in running order is ______ %.
Explanation / Answer
MTTR = 1/2 day
MTTF = 6 day
Availability, A = MTTF/(MTTF+MTTR) = 6/(6+1/2) = 0.923
Therefore, probability of any tower being in running order, p = 0.923
Probability that at least 13 towers will be in running order = P13 + P14 + P15 + P16
= 16C13*0.92313*(1-0.923)(16-13) + 16C14*0.92314*(1-0.923)(16-14) + 16C15*0.92315*(1-0.923)(16-15) + 16C16*0.92316*(1-0.923)(16-16)
= 0.09004 + 0.23154 + 0.37046 + 0.27785
= 0.9698 or 96.98 %
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.