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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 %