Is this question ambiguously worded?

A student asked me to explain this question from a previous year (high school) exam paper today. Fundamentally the question itself if very straight forward, however I thought it was quite poorly worded and perhaps open to misinterpretation. I'm wondering if anyone else thinks it a little ambiguous or if it's just me.

Heres the question.

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The manufacturer’s specifications state that the life of their light globes is normally distributed with a standard deviation of 170 hours.

What is the mean life, in hours, of these light globes if 97.5% will last up to 5000 hours?

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The thing that I don't like about this question is that longevity specifications are usually in the form of "9x percent will last at least y hours, whereas here they seem to be saying that they will last at most this many hours.

Does anyone else think that statement "if 97.5% will last up to 5000 hours" could have been better worded. I interpreted it as meaning that 97.5% will last at most 5000 hours but I'm wondering if anyone else here might have interpreted it the other way around?

matt grime
Homework Helper
There is nothing ambiguous about it: your point would seem to be that the person doing the question wouldn't read the words properly but assume they followed some format.

There is nothing ambiguous about it: your point would seem to be that the person doing the question wouldn't read the words properly but assume they followed some format.
Yeah I suppose that's about it. I thought the (unambiguous) answer was 5000 - 2s = 4660 hours but somehow couldn't help feeling that a lot of students might have mis-interpreted it and got an answer of 5000 + 2s instead.

D H
Staff Emeritus
I can certainly see the ambiguity. Advertisers see this also: How many commericials use "Up to" to obfuscate? The "at least" and "at most" are much less ambiguous.

If you want to make the students think a little, how about "Only 2.5% will burn out before 5000 hours pass" (mean is 5000 hours plus two sigma) or "2.5% will last longer than 5000 hours" (mean is 5000 hours minus two sigma). The number 97.5% is no longer present to smack the students upside the head and shout out "Think two sigma! Think two sigma!" to the students.

There is nothing ambiguous about it: your point would seem to be that the person doing the question wouldn't read the words properly but assume they followed some format.
No Matt it's more than just that. In most contexts I would interpret "up to x" as unambiguously meaning "not more than x" and this is how I originally interpreted the question.

Now however I'm suspecting that when the author wrote "97.5% will last up to 5000 hours" that they really did mean that 97.5% will still be operational at 5000 hours, which would give it the exact opposite meaning to what I originally thought.

It's a horribly worded question.

Does lightbulb longevity follow a normal distribution?

To me, it clearly says that only 2.5% will last longer than 5000 hours. I've done technical specs for decades and would never write something that fuzzy, but that would be the most likely legal interpretation.

CRGreathouse
Homework Helper
Does lightbulb longevity follow a normal distribution?
I would expect a bathtub curve, actually.

And, in truth, no manufacturer of light bulbs would be likely to use the phrase "normal distribution" since Weibull is almost universely used for such purposes.

D H
Staff Emeritus
It's a horribly worded question.
I agree. A light bulb manufacturer that claimed in an ad that 99.9999% of their bulbs last up to 100,000 hours would be slapped with a fine for deceptive advertising.

And, in truth, no manufacturer of light bulbs would be likely to use the phrase "normal distribution" since Weibull is almost universely used for such purposes.
So what? Stop being a pedant.

I agree. A light bulb manufacturer that claimed in an ad that 99.9999% of their bulbs last up to 100,000 hours would be slapped with a fine for deceptive advertising.

So what? Stop being a pedant.
Crabby this morning, aren't we?