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Math Help - Normal Distribution Problem

  1. #1
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    Normal Distribution Problem

    If the life, in years, of a television set is normally distributed with a mean of 35 years and a standard deviation of 8 years, what should be the guarantee period if the company wants less than 3% of the television sets to fail under warranty?

    I know how to set up the curve with the mean and standard deviation, but the 3% is throwing me off?

    Can anyone please help?

    Thanks
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  2. #2
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    the 3% would imply that it wants a 97% success rate. the Z corresponding to a value of 3% is 1.88.

    to find the appropriate value corresponding to that result:

     1.88=\frac{X-\mu}{\sigma} \rightarrow 1.88=\frac{X-35}{8} now just isolate for X.
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  3. #3
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    Quote Originally Posted by lion66 View Post
    If the life, in years, of a television set is normally distributed with a mean of 35 years and a standard deviation of 8 years, what should be the guarantee period if the company wants less than 3% of the television sets to fail under warranty?

    I know how to set up the curve with the mean and standard deviation, but the 3% is throwing me off?

    Can anyone please help?

    Thanks
    You already posted this here. Please do not double post.

    See Rule #1 of the forum.
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  4. #4
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    Where did you get the 1.88 from?

    Quote Originally Posted by lllll View Post
    the 3% would imply that it wants a 97% success rate. the Z corresponding to a value of 3% is 1.88.

    to find the appropriate value corresponding to that result:

     1.88=\frac{X-\mu}{\sigma} \rightarrow 1.88=\frac{X-35}{8} now just isolate for X.
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  5. #5
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    If you look at the the graph in the attachment, the blue area is the one associated with a 3% failure rate. So now we need to find the Z that goes with that 3%. We need to look at the normal distribution table to find the appropriate Z. So if you open the second attachment I have highlighted 3%, so we scroll left and up and realize that the value given is 1.88.
    Attached Thumbnails Attached Thumbnails Normal Distribution Problem-normal-dist.bmp   Normal Distribution Problem-normal_table.gif  
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