Uses of mean, standard deviation and Z tables

[sazzlefrazzle]

Hey i was wondering if anyone could help me with this question at all? I don't have a clue about the calculations and would be grateful if it could be explained to me! I'm really struggling! Thanks

Some light emitting diodes are tested and a sample is found to have a mean lifetime of 2048 hours and a standard deviation of 40 hours. The manufacturer wants to give a guaranteed lifetime for the LED’s on the box so that only 2% of the bulbs will be returned for not lasting for the guaranteed lifetime. Using Z table standard normal distribution show your calculation giving the lifetime he should put on the box.

 

[exk]

The question is asking you to find the lifetime X such that the probability of failure P(F) is less then or equal to .02.

 

[HallsofIvy]

Do you know how to change from a normal distribution with mean $\mu$ and standard deviation $\sigma$ to the standard normal distribution? If not, why in the world are you doing a problem like this?