Question

Prob-5 The lighting department of a city has installed 2000 electric lamps with an average life of 10,000 h and a standard deviation of 500 h. Alter what period of lighting hours would we expect 65.54% of the lamps to fall? Assume life of lamps are normally distributed, Ans: Sol:

Answer 1

Given that,

mean = $\mu$ = 10000

standard deviation = $\sigma$ =500

Using standard normal table,

P(Z > z) = 65.54%

= 1 - P(Z < z) = 0.6554

= P(Z < z ) = 1 - 0. 6554

= P(Z < z ) = 0.3446

= P(Z < -0.40) = 0.3446  

z = -0.40 (using standard normal (Z) table )

Using z-score formula  

x = z * $\sigma$ + $\mu$

x= -0.40*500+10000

x= 9800