A new type of light bulb called INCAND has a claimed mean lifetime of 1000 hrs w

Question

A new type of light bulb called INCAND has a claimed mean lifetime of 1000 hrs whereas a standard light bulb has a mean lifetime of 500 hrs. A set of comparative tests of INCAND and standard light bulbs is performed to assess whether INCAND has the claimed mean lifetime. Among other tests, a randomly selected INCAND and a standard bulb were first run for 500 hrs as a burn-in period. Assuming that the lifetimes of both bulbs are exponentially distributed, what is the difference in probability that INCAND will outlast the standard light bulb after a total run of 700 hrs if the claimed distribution for INCAND is true?

Explanation / Answer

Standard light bulb :

. so x~Exponetinal distribution with parameter 1/lamda=1/500=0.002

P(x>=700)=1-P(X<=700) = 1-=EXPONDIST(700,0.002,TRUE)=1-0.7534=0.2466

**** Using excel function =EXPONDIST(700,0.002,TRUE) to calculate the exponential probability.

INCAND :

x~Exponetinal distribution with parameter 1/lamda=1/1000=0.001

P(x>=700)=1-P(X<=700) = 1-=EXPONDIST(700,0.001,TRUE)=1-0.5034=0.4966

So difference in probability = 0.4966-0.2466 = 0.25

Hope this will be helpful. Thanks and God Bless You :-)

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