A system starts working at time t = 0. Its lifetime has approximately a normal distribution with mean value μ = 120 and standard deviation σ = 24 [hours]. After a failure, the system is replaced by an...

A system starts working at time t = 0. Its lifetime has approximately a normal distribution with mean value μ = 120 and standard deviation σ = 24 [hours]. After a failure, the system is replaced by an equivalent new one in negligible time and immediately resumes its work. How many spare systems must be available in order to be able maintain the replacement process over an interval of length 10,000 hours

(1) with probability 0.90,

(2) with probability 0.99?