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Find MIN number of light hours the company must set to replace 3% of the tubes.

Here's the full question:

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.

My working out:

https://i.imgur.com/PbiDpS6.jpg

The answer is 1970 hours.
(edited 6 years ago)
Reply 1
Avatar for Notnek
Notnek
21
Original post by Mathman69
Here's the full question:

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.

My working out:

https://i.imgur.com/PbiDpS6.jpg

The answer is 1970 hours.

You made a mistake near the beginning of your working. Think about the question : the mean duration is 2010 hours so the minimum duration obviously has to be lower than this. Can you see your mistake?

If you understand what's going on in this question then you should find your mistake.

By the way, your questions are going to have to continue to be approved for now if you post links. It would be better if you can post your working in your post so that a mod doesn't have to approve your post. Your working could be in plaintext or you might want to try using LaTeX
Reply 2
Avatar for Mathman69
Mathman69
OP
3
Original post by Notnek
You made a mistake near the beginning of your working. Think about the question : the mean duration is 2010 hours so the minimum duration obviously has to be lower than this. Can you see your mistake?

If you understand what's going on in this question then you should find your mistake.

By the way, your questions are going to have to continue to be approved for now if you post links. It would be better if you can post your working in your post so that a mod doesn't have to approve your post. Your working could be in plaintext or you might want to try using LaTeX

I don't understand what's going on in the question =/
I'm having trouble turning the given info into the language of the distribution. Here's the only other solutions I see:
P(Z>(m-2010)/20) = (1-0.03)
P(Z<(m-2010)/20) = (1-0.03)
P(Z<(m-2010)/20) = 0.03
Original post by Mathman69
Here's the full question:

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.

My working out:

https://i.imgur.com/PbiDpS6.jpg

The answer is 1970 hours.


The company only replaces the bulb when the bulb life is less than that promised. Using your definitions therefore you need to calculate m such that P(L<m) = 0.03. You are calculating P(L>m)=0.03
Reply 4
Avatar for Mathman69
Mathman69
OP
3
Original post by Towcestermaths
The company only replaces the bulb when the bulb life is less than that promised. Using your definitions therefore you need to calculate m such that P(L<m) = 0.03. You are calculating P(L>m)=0.03

Thanks! Is there different definitions I could use? The ones I came up with are very confusing.
Original post by Mathman69
Thanks! Is there different definitions I could use? The ones I came up with are very confusing.


I think the language used is, for many students, the most difficult part of these sort of questions. I can only advise to always draw a diagram and think carefully about what the question is asking. In this case, they are only going to give a replacement if the bulb life was less than that promised. Thus your point needs to be the one that will have 3% to the left of it. I hope that makes sense. Its hard to explain without a diagram in front of us.

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