
051406, 12:20 AM #1
Standard Deviation {help me understand statistics}
First of all, it's been a while since my last post  I'm back in college and super busy. I'm doing a take home test now in statistics and I'm completely stuck on one problem... hoping anyone can help, please
I've finished 24 of the 25 questions, double checked them all and I am sure that I have them all correct. However this question (#25) is frustrating me to no end  and I'm coming to you with humility and shame. I just don't understand what I am doing wrong. I'm not simply asking for an answer here; I truly want to understand what I'm screwing up, so I'll post my method and then you can point out my error.
Here goes...
The question:
A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distrubution approximated by a normal bell curve. Find the % of bulbs that can be expected to last between 540 hours and 780 hours.
My [wrong] answer:
First I had to obtains a zscore for each piece of data. To do this I subtracted the data from the mean and divided my answer by the standard deviation.
The zscore for 540 = (540500)/100 = .4
The zscore for 780 = (780500)/100 = 2.8
Then I took those zscores and figured out their respective areas on the curve [using a nifty chart in my textbook].
The Area of zscore .4 = .016
The Area of zscore 2.8 = .497
Finally, I subtracted The area .016 from .497
So: .497  .016 = .481
Multiply by 100 and the answer should be 48.1%, correct?
No...
My choices (it's a multiple choice exam) are 44.3%, 34.2%, 34.34%, and 44.34% !!!
My answer does not match.
I considered subtracting 48.1% for 50% since both scores are on the right side of the mean on the curve, but that didn't work either

Please help me. I am going crazy over this. I usually wouldn't ask for help on schoolwork, because I know this is not a "I'll do your schoolwork for you" sort of board, but I'm not asking anyone to simply give me an answer. I really want to understand my mistake and what I am doing wrong.
Thanks.

051406, 12:48 AM #2
Provided your areas are correct, I would say your answer is right.

051406, 12:25 PM #3
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 2,257
Originally Posted by sevenblu
Then I took those zscores and figured out their respective areas on the curve [using a nifty chart in my textbook].
The Area of zscore .4 = .016
The Area of zscore 2.8 = .497
 50% of the population lies below the mean, so certainly more than 50% of the population lies below the mean plus 0.4 standard deviations.
 2.8 is nearly 3, and 99.87% of the population lies below the mean plus 3 standard deviations.
My choices (it's a multiple choice exam) are 44.3%, 34.2%, 34.34%, and 44.34% !!!
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