Answer to Question #277585 in Statistics and Probability for Coffee

Question

The local administration installed 3500 Incandescent bulbs as part of a new lighting system project. According to them, the bulbs are produced by several companies and have a burn time of 1060 hours on average. The distribution of the burning lives is close to normal. They discovered that the 350th light bulb had burned out after 822 hours of observation. What is the standard deviation of the burning lives of this set of lightbulbs? 

Answer 1

350th light bulb had burned out after 822 hours of observation means that:

$P(x<822)=0.1$

then:

$z=-1.28=\frac{x-\mu}{\sigma/\sqrt n}$

$\sigma=\frac{1060-822}{1.28/\sqrt {3500}}=11000.21$