Normal distribution: lifetimes of new halogen lights

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

PCmaster said:

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

Click to expand...

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%?

Ishuda said:

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%?

Click to expand...

Sorry I still don't understand can you walk me through it.

PCmaster said:

Sorry I still don't understand can you walk me through it.

Click to expand...

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!!")