The life expectancy (in hours) of a fluorescent tube is normally distributed with a mean 8000 and a standard deviation 1000. find the probability that a tube lasts for more than 11000 hours.

Given that the, mean is 8000 and the standard deviation is 1000, thus the probability that tube lasts for more than 11000 hours. will be given by:

P (x>11000)

the z-score is:

z = (x - μ) / σ

x=11000

μ=8000

σ=1000

hence:

z = (11000-8000) / 1000

z=3

thus

P (x>11000) = 1-P (x<11000)

But

P (x<11000) = P (z<3) = 0.9987

hence

P (x>11000) = 1-0.9987=0.0013