I'm trying to find the approximate percentile rank of a lightbulb that failed at
9000 hours (based on the information from the problem below), but I'm not sure how to solve this...
A consumer product testing lab tested 400 13-watt compact
fluorescent light bulbs by turning them all on at once, leaving them
on until they burned out, and recording the time-to-failure of each
bulb. The test revealed a symmetric and mound-shaped
distribution of times-to-failure with mean 7800 hours and standard
deviation 1200 hours. The number of lightbulbs that lasted between 5400 and 9000 hours were about 326 lightbulbs.
This is my guess:
percentile = 7800/9000 = about 86%, since 9000 hours is 1 standard deviation from the mean