A cutting tool wears out with a time to failure that is normally distributed with a mean of 10 working days and a standard deviation of 2.5 days.
(a) Determine its design life for a reliability of 0.99.
(b) Find the reliability if the tool is replaced every (i) day; (ii) two days; (iii) three days. Find R(1), R(2), and R(5)
(c) Determine the probability that the cutting tool will last one more day given it has been in use for 5 days.