Fewer than percentage distribution plot: battery lifespan

Elemental

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Oct 21, 2016
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Hello! Posting this here cause my girlfriend is having trouble with a math problem and I can't really figure out what to do either.

A manufacturer of batteries tested the lifespan of a sample of batteries. Mean life was found to be 485 days with standard deviation of 26 days. These batteries are used in beacons that are switched off for 10 hours a day. After how many days should the batteries be changed to ensure that less than 2% of the beacons experience battery failure.

Now I tried attacking this from several angles but basically had to resort to guesstimating values of the Z against a plot, and they expect her to do it without a graphical calculator. She does have a normal distribution Z table for reference though.

Thanks for your help!
 
A manufacturer of batteries tested the lifespan of a sample of batteries. Mean life was found to be 485 days with standard deviation of 26 days. These batteries are used in beacons that are switched off for 10 hours a day. After how many days should the batteries be changed to ensure that less than 2% of the beacons experience battery failure.

Posting this here cause my girlfriend is having trouble with a math problem and I can't really figure out what to do either.
Please have the actual student reply, showing what she has tried, outlining what her thoughts are, and clarifying where she is stuck. Thank you! ;)
 
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