Math Is Fun Forum

cathelyn13

Member

Registered: 2009-07-18

Posts: 10

Question on Normal Distribution

The fluorescent light tubes made by the company Well-lit have lifetimes which are normally distributed with mean 2010 hours and standard deviation 20 hours. The company decides to promote its sales of the tubes by guaranteeing a minimum life of the tubes, replacing free of charge any tubes that fail to meet this minimum life. If the company wishes to have to replace free only 3% of the tubes sold, find the guaranteed minimum it must set.

What I did was:
Let A be the minimum number of hours,
(A - 2010) / 20 = -1.8808
A = (-1.8808 * 20) + 2010 = 1972.384
So my answer is 1972 hours. However, the answer provided by the book is 1970 hours but I only can get 1972.384.. If anyone can get 1970, how did you arrive to that answer?

Thanks in advance!! 

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Question on Normal Distribution

Hi cathelyn13;

  I am drawing a blank here because I am getting the same answer that you are. What is the name of the book?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

cathelyn13

Member

Registered: 2009-07-18

Posts: 10

Re: Question on Normal Distribution

It's Advanced Level Mathematics Statistic 1 by Steve Dobbs & Jane Miller.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Question on Normal Distribution

Hi cathelyn13;

I was looking for errata on that book. Does the book mention a site where you can check for corrections because it could be a typo.

You have convinced me! I think you have correctly computed the z score as ≈ -1.8808. This also does look like a one tailed test. I don't know why the book answer has 2 standard deviations from the mean rather than 1.8808 standard deviations . Sorry, I couldn't help out. If you find the answer please come back and tell me.

Last edited by bobbym (2009-07-18 03:13:39)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Question on Normal Distribution

It looks like they just "rounded".  Companies don't advertise exact figures, typically they make it a more appealing figure by putting a zero (or more) in some digits.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

cathelyn13

Member

Registered: 2009-07-18

Posts: 10

Re: Question on Normal Distribution

I see. Thanks a lot!! Should be it. Hehe!