• Welcome! The new FreeMathHelp.com forum is live. We've moved from VB4 to Xenforo 2.1 as our underlying software. Hopefully you find the upgrade to be a positive change. Please feel free to reach out as issues arise -- things will be a little different, and minor issues will no doubt crop up.

Normal distribution: lifetimes of new halogen lights

PCmaster

New member
Joined
Jan 18, 2015
Messages
5
Question

A manufacturer sells a new halogen light, the lifetimes of which are normally distributed with a mean weight of 1400 and standard deviation of 50 hours.

It is intended that 90% of the lights should last longer time of T hours. What is the value of T.


Answer

P(Z<1.2816) Taken from the table
t= 50 x 1.2816 + 1400
t= 1464.08


is this correct
 

Ishuda

Elite Member
Joined
Jul 30, 2014
Messages
3,345
Question

A manufacturer sells a new halogen light, the lifetimes of which are normally distributed with a mean weight of 1400 and standard deviation of 50 hours.

It is intended that 90% of the lights should last longer time of T hours. What is the value of T.


Answer

P(Z<1.2816) Taken from the table
t= 50 x 1.2816 + 1400
t= 1464.08


is this correct
That is the flip side of the question. 90% of the lights will fail before 1464.08 hours. Since the mean is 1400 hours, 50% will fail before 1400 hours so your answer has to be less than 1400 hours.

So if we have the tail of greater than 90% is at Z=+1.2816, what is Z at the tail for less than 10%?
 

PCmaster

New member
Joined
Jan 18, 2015
Messages
5
That is the flip side of the question. 90% of the lights will fail before 1464.08 hours. Since the mean is 1400 hours, 50% will fail before 1400 hours so your answer has to be less than 1400 hours.

So if we have the tail of greater than 90% is at Z=+1.2816, what is Z at the tail for less than 10%?
Sorry I still don't understand can you walk me through it.
 

stapel

Super Moderator
Staff member
Joined
Feb 4, 2004
Messages
15,937
Sorry I still don't understand can you walk me through it.
If half of them will fail by the 1400-hour mark, then only 50% of them will still be working by that time. You are asked to find the time (the number of hours) by which 90% of the bulbs will still be working.

If only 50% are working by 1400 hours, you cannot possible have more working (coming back to life somehow?) at a later time. You can only have fewer working after the 1400-hour mark.

In other words, I think you've been trying to work with the failure rate: finding the time by which 90% would have failed. This will, of course, be after the 1400-hour mark. But you've been asked to find the success rate: finding the time by which 90% will still be working. (This is useful for advertising, so you can promote your bulbs as having an expected lifetime of T hours "or more!!") ;)
 
Top