No Leak Plumbing and Repair provides customers with firm quotes for a plumbing repair job before actually starting the job. To be able to do this, No Leak has been very careful to maintain time records over the years. For example, it has determined that the time it takes to remove a broken sink disposal and to install a new unit is normally distributed with a mean equal to 47 minutes and a standard deviation equal to 12 minutes. The company bills at $75.00 for the first 30 minutes and $2.00 per minute for anything beyond 30 minutes.
Suppose the going rate for this procedure by other plumbing shops in the area is $85.00, not including the cost of the new equipment. If No Leak bids the disposal job at $85, on what percentage of such jobs will the actual time required exceed the time for which it will be getting paid?