Stat 101: CLT
Light bulb data
- Accelerated life testing. (By using overvotage, you can
simulate 10,000 hours of life in a few hours of real time.)
- Each minute a sample bulb is pulled from the production line
- It is tested and recorded
- Goal: 1000 hours average life--but want to "know" it is over
900 hours (so within 10 percent of target)
- If we test a few bulbs and stop production whenever our average
is less than 900 hours, how often do we cry "wolf"?
- What is the distribution of the average? (This is a hard problem)
- But if we average enough, it looks normal
Key points
- Standard deviation goes down as 1/sqrt(n)
- Shape gets more normal as n increases
Problem
- Suppose we want to be 6-sigma sure of being over 900 hours by
chance alone. How many bulbs should we collect?
- Note: 6-sigma for normal is .000 000 002 or 1/500 Million!
Last modified: Wed Nov 17 10:18:56 EST 1999