a company installs 5000 light bulbs, each w/ an average life of 500 hours, standard deviation of 100 hours and distribution approximated by a normal curve. Find the percentage of bulbs expected to last the period of time?
1)less than 500 hours
2)between 540 hours & 780 hours
1)less than 500 hours
2)between 540 hours & 780 hours
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Hello,
1) Since the mean is 500, 1/2 of them would last less than 500 hr.
2) 540 is .4 SD from the mean n = (540 -500) /100 = 0.4 so we look up z of 0.4 = 0.6554
780 is 2.8 SD from the mean m = (780-500)/100 = 2.8 looking up z of 2.8 gives us 0.9974
So we want the percent in between these hence: 0.9974 - 0.6554 = 0.3420 as a percent 34.20%
Hope This Helps!
1) Since the mean is 500, 1/2 of them would last less than 500 hr.
2) 540 is .4 SD from the mean n = (540 -500) /100 = 0.4 so we look up z of 0.4 = 0.6554
780 is 2.8 SD from the mean m = (780-500)/100 = 2.8 looking up z of 2.8 gives us 0.9974
So we want the percent in between these hence: 0.9974 - 0.6554 = 0.3420 as a percent 34.20%
Hope This Helps!
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1) Half of them.
2) 540 is 500 plus (40/100) sd's, and 780 is 500 plus (280/100) sd's.
The z-score for 0.4 is .6554 and the z-score for 2.8 is .9974.
.9974 - .6554 = 0.342.
34.2% of the bulbs will last between 540 and 780 hours.
2) 540 is 500 plus (40/100) sd's, and 780 is 500 plus (280/100) sd's.
The z-score for 0.4 is .6554 and the z-score for 2.8 is .9974.
.9974 - .6554 = 0.342.
34.2% of the bulbs will last between 540 and 780 hours.