Failure in optical fibers used in communications systems are typically due to a brittle fracture that grows into a complete crack, thereby disrupting transmission. Currently, carbon furnaces are used to heat treat the fibers, which have a 4.5% failure rate. Engineers are considering switching to laser heating if it can be demonstrated that this reduces the fiber failure rate. Lete p denote the fiber failure probability using laser heat treating.
One hundred and eighty fibers are produced with laser heating and tested. Of 180 fibers tested, 6 failed.
Let P denote the probability of failure
Construct a 95% confidence interval for p.