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In: Statistics and Probability

The lives of certain extra-life light bulbs are normally distributed with a mean equal to 1350...

The lives of certain extra-life light bulbs are normally distributed with a mean equal to 1350 hours and a standard deviation equal to 18 hours. 1. What percentage of bulbs will have a life between 1350 and 1377 hr? 2. What percentage of bulbs will have a life between 1341 and 1350 hr? 3. What percentage of bulbs will have a life between 1338 and 1365 hr? 4. What percentage of bulbs will have a life between 1365 and 1377 hr? 5. What percentage of bulbs will have a life between 1338 and 1344 hr? 6. What percentage of the bulbs will last longer than 1386 hr? 7. What percentage of the bulbs will last less than 1323 hr? 8. The 10 percent of the bulbs with the longest life will last longer than how many hours? 9. The 20 percent of the bulbs with the shortest life will last no longer than how many hours?

I am looking for help with 7-9. Looking for the math worked out, to find the answer. Thanks

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The lives of certain extra-life light bulbs are normally distributed with a mean equal to 1350 hours and a standard deviation equal to 18 hours. 1. What percentage of bulbs will have a life between 1350 and 1377 hr? 2. What percentage of bulbs will have a life between 1341 and 1350 hr? 3. What percentage of bulbs will have a life between 1338 and 1365 hr? 4. What percentage of bulbs will have a life between 1365 and 1377 hr? 5. What percentage of bulbs will have a life between 1338 and 1344 hr? 6. What percentage of the bulbs will last longer than 1386 hr?

7. What percentage of the bulbs will last less than 1323 hr?

Z value for 1323, z = (1323-1350)/18 = -1.5

P( x <1323) = P( z < -1.5) =0.0668

The required percentage = 6.68%

8. The 10 percent of the bulbs with the longest life will last longer than how many hours?

Z value for top 10% = 1.282 ( from standard normal distribution)

X= mean+z*sd = 1350+1.282*18

=1373.076

9. The 20 percent of the bulbs with the shortest life will last no longer than how many hours?

Z value for bottom 20% = -0.842 ( from standard normal distribution)

X= mean+z*sd = 1350-0.842*18

=1334.844

I am looking for help with 7-9. Looking for the math worked out, to find the answer. Thanks

orchestra answered 1 year ago
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