fluorescent light bulbs last, on average 10,000 hpurs. the standard diviation is 500 hours.what percent of the light bulbs burn out within 11,000 hours?

Question

 i need to find out what percent of lightbulbs burn out within 11,000 hours

Answer 1

The implicit assumption here is that the bulb lifetime is normally distributed.   The fraction of bulbs that burn out within 11000 hours is the area under the relevant normal curve between - ∞ and 11000.  

 

The easiest way to get a numerical answer is to use a graphing calculator such as the TI-84,

 

On the TI-84  , enter DISTR (2nd VARS),  select 2: normalizedcdf , fill in lower = - 1E99 , upper = 11000, μ = 10000, σ = 500.   Scroll down to PASTE and hit enter twice.      The answer comes out to be .97725.   This means that 97.7 % of the bulbs will burn out within 11000 hours.

 

The TI calculator is setting up an normal distribution with mean = 10000 and standard deviation = 500, then integrating from a very large negative number (essentially - ∞) to 11000.   The function normalcdf is essentially the definite integral of the normal curve (bell curve)