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A outdoor light bulb has an expected (mean) life of 8,000 hours with a standard deviation of 250 hours. How many bulbs in a batch of 500 can be expected to last no longer than 7500 hours?

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  • $\begingroup$ This website works better if you show us how far you got, where you got stuck, and so on. $\endgroup$ Mar 6 '14 at 6:19
  • $\begingroup$ I just got to subtracting 7500 from 8000 and figured on 1st standard dev. and 2nd standard dev. but had no clue with what to do withe the # 500-thanks for your help $\endgroup$
    – Amy
    Mar 7 '14 at 4:04
  • $\begingroup$ OK, I think you are saying you worked out that 7500 hours is 2 standard deviations below the mean. Have you learned how to figure out what percentage of a sample is 2 or more standard deviations below the mean? $\endgroup$ Mar 7 '14 at 11:38
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Hint:

$$ P(X<=7500) = P(z<=\frac{(7500-8000)}{250})$$

$$ P(X<=7500) = P(z<=-2) = 0.02275$$

Expected number of bulbs in a batch of 500 that will not last longer than 7500 $$= .02275*500 = 12 bulbs$$

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