Question

"SUPERCALIFRAGILISTICOEXPIALIDOSO" is a manufacturing company of resistors which are known to have an exponential failure rate distribution.

Failure rate = 9.09 x 10^-5

a) Given that a resistor has been working for 4,500 hours, what would be the probability that it would survive 2000 hours more of use?

b) What is the probability any resistor will still be working after 6000 hours of use?

c) At what point in time will 20% of these resistors be expected to still be working?

d) What is the probability it will fail within 5000 hours of use?

Answer 1

here for exponential distribution parameter λ =9.09*10-5

P(X<x) =1-e^-λx

a)

P(X>6500|X>4500) =e^{-6500*9.09*10^-5}/e^{-4500*9.09*10^-5} =e^{-2000*9.09*10^-5} =0.8338

b )

P(X>6000)=1-P(X<6000)=1-(1-e-6000*9.09*10^-5=

0.5796

c)

since at 80th percentile, 20 % of the bulbs are still be working:L

pth percentile =-ln(1-p)/λ

therefore 80th percentile =-(1/9.09*10-5)*ln(1-80/100)=

17705.59 Hours

d)

P(X<5000)=1-e-5000*9.09*10^-5=0.3652