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Math Help - 68-95-99.7 Rule Help

  1. #1
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    68-95-99.7 Rule Help

    A company produces lightbulbs. The lifetimes (in hours) of lightbulbs have a normal distribution with a mean of 1200 hours and a standard deviation of 50 hours. Use the 68-95-99.7 rule to answer the following questions:

    (a) 84% of the lightbulbs burn out before how many hours?
    (b) 0.15% of the lightbulbs burn out before how many hours?
    (c) 97.5% of the lightbulbs last longer than how many hours?

    My Attempt: (Using the mean - sigma equation)
    (a) 1200 - 2 * 50 = 1100 hours
    (b) 1200 - 3 * 50 = 1050 hours
    (c) 1200 + 3 * 50 = 1350 hours

    I don't think I did this right but if someone could explain to me how to solve this problem I would be very thankful!
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  2. #2
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    Re: 68-95-99.7 Rule Help

    Quote Originally Posted by michellederz View Post
    A company produces lightbulbs. The lifetimes (in hours) of lightbulbs have a normal distribution with a mean of 1200 hours and a standard deviation of 50 hours. Use the 68-95-99.7 rule to answer the following questions:

    (a) 84% of the lightbulbs burn out before how many hours?
    (b) 0.15% of the lightbulbs burn out before how many hours?
    (c) 97.5% of the lightbulbs last longer than how many hours?

    My Attempt: (Using the mean - sigma equation)
    (a) 1200 - 2 * 50 = 1100 hours
    (b) 1200 - 3 * 50 = 1050 hours
    (c) 1200 + 3 * 50 = 1350 hours

    I don't think I did this right but if someone could explain to me how to solve this problem I would be very thankful!
    a) 84% is 1 sigma above the mean. This would be 1200 + 50 = 1250 hrs.

    b) 0.15% is 3 sigmas below the mean, i.e. 1200 - 3*50 = 1050 hrs, you did this correctly

    c) 97.5% is about 2 sigmas above the mean i.e. 1300 hrs
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  3. #3
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    Re: 68-95-99.7 Rule Help

    Quote Originally Posted by romsek View Post
    a) 84% is 1 sigma above the mean. This would be 1200 + 50 = 1250 hrs.

    b) 0.15% is 3 sigmas below the mean, i.e. 1200 - 3*50 = 1050 hrs, you did this correctly

    c) 97.5% is about 2 sigmas above the mean i.e. 1300 hrs
    Oh! This makes sense.
    So when I create the graph, will I shade in 85% of the area to the right or left of the mean for part a? I shaded in coming from the left side of the graph and it goes 1 standard deviation over the mean. Is this correct?
    Last edited by michellederz; February 5th 2014 at 08:13 PM.
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  4. #4
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    Re: 68-95-99.7 Rule Help

    68-95-99.7 Rule Help-clipboard01.jpg

    the blue area is what you want.
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  5. #5
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    Re: 68-95-99.7 Rule Help

    Quote Originally Posted by romsek View Post
    Click image for larger version. 

Name:	Clipboard01.jpg 
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ID:	30127

    the blue area is what you want.
    Perfect, that is what I have down. However, I believe part c is wrong. Could it possibly be 1350? I asked my professor if 1300 was right and he told me no but will not tell me why.
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  6. #6
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    Re: 68-95-99.7 Rule Help

    Ok, my bad. I didn't read the question carefully enough.

    You want the number that 97.5% of the bulbs last longer than.

    That means you want the value corresponding to 100% - 97.5% = 2.5%

    This is about 2 sigmas below the mean or 1200 - 2*50 = 1100 hrs.
    Last edited by romsek; February 5th 2014 at 09:08 PM.
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