# Thread: Standard Deviation {help me understand statistics}

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.

First I had to obtains a z-score for each piece of data. To do this I subtracted the data from the mean and divided my answer by the standard deviation.

The z-score for 540 = (540-500)/100 = .4
The z-score for 780 = (780-500)/100 = 2.8

Then I took those z-scores and figured out their respective areas on the curve [using a nifty chart in my textbook].

The Area of z-score .4 = .016
The Area of z-score 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% !!!

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

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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.

3. Originally Posted by sevenblu

First I had to obtains a z-score for each piece of data. To do this I subtracted the data from the mean and divided my answer by the standard deviation.

The z-score for 540 = (540-500)/100 = .4
The z-score for 780 = (780-500)/100 = 2.8
Ok so far.

Then I took those z-scores and figured out their respective areas on the curve [using a nifty chart in my textbook].

The Area of z-score .4 = .016
The Area of z-score 2.8 = .497
Whoa! How do you get that? These answers don't make any sense. Think abut it this way:
- 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% !!!
One of those choices is indeed correct.

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