A cutting tool wears out with a time to failure that is normally distributed with a mean of 10…

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) five days.

(c) Determine the probability that the cutting tool will
last one more day given it has been in use for 5 days.