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17 January, 00:22

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.

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  1. 17 January, 00:27
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    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
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