Question

The lifetime of a particular brand of lightbulb is a normally-distributed variable with a mean of 10300 hours and a standard deviation of 320 hours. The longest-working 15% of lightbulbs will work for at least how many hours?

Answer 1

Given that,

mean = = 10300

standard deviation = =320

Using standard normal table,

P(Z > z) = 15%

= 1 - P(Z < z) = 0.15

= P(Z < z ) = 1 - 0.15

= P(Z < z ) = 0.85

= P(Z < z ) = 0.85

z =1.04 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 1.04*320+10300

x= 10632.8