Answer to Question #138263 in Statistics and Probability for ASHISH

Question

CFL bulb of a certain make have a mean life of 800 hours with S.d. of 150 hours. Out of 50 thousand bulbs of that make used for street lighting, how many of them would fuse in first 650 hours, if the distribution of the life of bulbs is assumed to be normal? How Many bulbs would be burning after 950 hours?

Answer 1

$Given \; that, μ=800, σ=150, then,\\ a) P(x<650) = P( Z <\frac{650-800}{150})\\ =P(Z<-1)\\=0.5- P(0<Z<1)=0.5-0.3413=0.1587\\ \text{number of bulbs }=50000\times 0.1587=7935\;bulbs \\ b) P(x>950) = P( Z >\frac{950-800}{150})\\ =P(Z>1)\\=0.5- P(0<Z<1)=0.5-0.3413=0.1587\\ \text{number of bulbs }=50000\times 0.1587=7935\;bulbs$