Question 1139689: A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve. Find the percentage of bulbs that can be expected to last the period of time. Round to the nearest hundredth, if necessary.
Less than 520 hours
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! mean is 500 hours.
standard deviation is 100 hours.
number of light bulbs installed is 5000.
z = (x - m) / s
z is the z-score
x is the raw score
m is the raw mean
s is the standard error, which, in this case, is the standard deviation, since you are dealing with the population of 5000 light bulbs rather than a sample of a much larger population.
in this problem, the formula becomes z = (520 - 500) / 100.
solve for z to get z = 20 / 100 = .2
with a z-score of .2, the percentage of bulbs that can be expected to last less than 520 hours would be equal to .5792596878 * 100 = 57.92596878%.
round to 2 decimal places and the solution is 57.93%
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