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**struck** The fluorescent light tube made by the company have lifetimes which are normally distrubted with mean 2010 hours and standard deviation 20 hours. The company decides to promote its sales of the tubes by guaranteeing a minimum life of the tubes, replacing free of charge any tubes that fail to meet this minimum life. If the company wishes to have to replace free only 3% of the tubes sold, find the guaranteed minimum it must set.

Let L = life, and u = mean life, and o = standard deviation.

We have:

L ~ N(2010, 20^2)

Let Z = (X - 2010) / 20 ... Then Z ~ N(0,1).

I tried it this way, but it won't work. Not sure why is the following wrong:

$\displaystyle P(L > -0.97) = 1 - \phi (0.97)$

Please let me know the correct way with some explanation as I need to figure it out.