Question 252139: 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 between:
a) 290 hours and 500 hours.
b) 540 hours and 780 hours.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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 between:
a) 290 hours and 500 hours.
Find the fraction of population between those limits.
z(290) = (290-500)/100 = -2.1
z(500) = (500-500)/100 = 0
normalcdf(-2.1,0) = 0.4821
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%age = 0.4821*5000 = 2410.67
Rounding down = 2410
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b) 540 hours and 780 hours.
z(540) = (540-500)/100 = 0.4
z(780) = (780-500)/100 = 2.8
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P(540 < x < 780) = P(0.4 < z < 2.8) = 0.3420..
%age = 0.3420*5000 = 1719
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Cheers,
Stan H.
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