Trouble-free working time of medical robots

1) Look up the quantile function of the lognormal distribution (you can use the formula directly in excel) and get

T=59.00798 months

about 59 months

2)

LogNorm(59,6,1.5)=90.0%

LogNorm(60,6,1.5)= 89.8%

So the probability of not being repaired and still functioning in the next month = 89.8%/90.0%=99.8%