Question

The lighting department of a city has installed 2000 electric lamps with an average life of 1000 hrs and a standard deviation of 200 hrs. (10 Points) a. After what period of lighting hours would we expect 10% of the lamps to fail? b. How many lamps may be expected to fail between 900 and 1300 hrs?

Answer 1

Answer

given,

installed electric lamp = 2000

average life = 1000 hrs

standard deviation = 200 hrs

a)

let after p hors 10% bulb fails ,

P(X<p) = 0.10

$P(X< \dfrac{x-\mu}{\sigma})= 0.10$

from Normal distribution table,

P(Z<-1.28) = 0.10

on comparing

$\dfrac{x-\mu}{\sigma} = -1.28$

$\dfrac{x-1000}{200} = -1.28$

x = -1.28 x 200 + 1000

x = 744 hours

b)    P( 900 < X < 1300) =

 =$P(\dfrac{900 -1000}{200} < Z$

 = P(-0.5 < Z < 1 .5)

 = P(Z<1.5) - P(Z<-0.5)

  = 0.93319 - 030854

 = 0.62465

lamps may be expected to fail between 900 and 1300

= 0.62465*2000

= 1249.3

= 1249 (approx)