It is estimated that the mean life span of oil-drilling bits is 75 hours. Suppose an oil exploration company purchases drill bits that have a life span that is approximately normally distributed with a mean equal to 75 hours and a standard deviation equal to 12 hours.
a. What proportion of the company's drill bits will fail before 60 hours of use?
b. What proportion will last at least 60 hours?
c. What proportion will have to be replaced after more than 90 hours of use?