Help - I think I'm right

[DiceyPlay]

I'm a math tutor at a nearby college. I was reviewing a test with a student and came across a problem I thought the student had done right but the teacher marked it wrong. I emailed the teacher. Here is a copy of the email I sent to the teacher:

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Hi,

My name is Michael xxxxxxx. I am a tutor in the tutorial center at XYZ. I reviewed an exam or quiz with a student. The exam or quiz was given this semester in a statistics class you are teaching. In particular question #9 is worded as follows:

A used car dealership has found the length of time before a major repair is required on the cars it sells is normally distributed with mean equal to 10 months and standard deviation of 3 months. If the dealer wants only 5% of the cars to fail before the end of the guarantee period, how many months should the car guarantee be?

The student gave an answer of 5 months. The students answer was marked wrong and a correct answer of 15 was indicated.

If one recommends a quarantee period (15 months) that is greater then the mean time (10 months) until a major repair is required, we should expect more than 50% of the cars to come back for service under the guarantee.

Let x be a random variable with distribtion as described in the question above. 95.15% of the area under the curve lies to the left of x=15. This means that, on average, 95.15% of the cars will require major repair within 15 months.

The more I look at this the more I convince myself that the students answer is correct. Am I looking at this wrong somehow?

A reply is greatly appreciated.

Kind and respectful regards,

-Michael

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Here is the reply I received from the teacher:

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Hello Michael,

Yes, at first glance 5 months seems like a correct answer. Actually when I did the problem first myself I got that answer!
But let me reword the problem.
Let's say that on average it takes 10 months for an average person to finish a training program and successfully pass a test, with SD of three months. If you want to make sure(guarantee) that 95% of the people enrolled will pass the test, how many months should the program last? You see 5 months does not make sense.

You want only 5% of the cars to fail or 95% not fail. If you set up the problem the way that you have, 95% of the cars fail and only 5% will not have problems.

Hope this helps,

Kia

----------------------------------------

To me he's changing the problem. Of course one could construct a different problem where a random variable has the same distribution and the answer is different. I don't know how to make it any more clear than with what I wrote to him.

Or maybe I'm just flat wrong. But I obviously don't think so. Can someone either explain it to me or show me a way to explain to him so he can see the error in his ways?

Thanks ... your help is greatly appreciated.

-Michael

[Victor]

so hes saying that 95% of cars will fail after 5mo? but the mean failure time is 10mo?

[Colima420]

I think that the professor made a typo and the problem should have been stated as:

"A used car dealership has found the length of time before a major repair is required on the cars it sells is normally distributed with mean equal to 10 months and standard deviation of 3 months. If the dealer wants only 5% of the cars to fail AFTER the end of the guarantee period, how many months should the car guarantee be? "

First of all, it wouldn't make sense for a dealer to want the mayority of his cars (95%) to fail when the customers don't have the guarantee. It only makes sense for the dealer to want only 5% of cars to fail after the guarantee. This way the guarantee actually works. If 95% of cars need repairs after the guarantee is over, then the guarantee has no purpose.

Secondly, if we analyze his example of his reply to you (regarding the time it takes a person to complete a course), it is almost identical to the car problem with the AFTER word in it.

This way,


z = (x - mu) / sigma

The z critical value for .05 (probability of car failure, since he wants 5%) is 1.645. This can be found in any z table.

now if we solve the previous equation with this number we get:

1.645 = (x - 10) / 3
4.935 = x - 10
14.935 = x Rounding up we get x = 15. We need to have the guarantee to be for 15 months in order to have 5% of all cars fail after that.

So my whole theory is that the original problem should have been: "How many months should the guaranteee be in order to have 5% of the cars not be covered by it?"

or conversely: "How many months should the guarantee be for in order to have 95% of the cars covered by it"?

Colima420

[ojc02]

Yeah, I agree this must have been the intention. The student answered the question correctly and frankly, the original question makes more sense. The dealership is likely to want most of the cars to fail after the end of the warranty.

It is totally unreasonable of the professor to change the wording of the problem so drastically afterwards. The student provided the correct answer to the question posed.

[madnak]

You're right, teacher is wrong.

[DiceyPlay]

Let me know if you're interested and I'll make sure I post the results or the on-going saga.

Here is my response to his reply.

Hi Kia,

I'm not sure how to respond to your reply. But stating a different problem does not help. Discussing the similarities and dis-similarities between the two problems simply would not be fruitful. Let's stick with the original problem. I thought my argument was clear and compelling. Let's try again.

1) Intuitively - longer guarantee periods result in more cars being covered under the guarantee.

2) A mean failure time of 10 months suggests 50% the cars fail before 10 months and 50% the cars fail after 10 months (normal distribution -- median = mean).

Putting (1) and (2) together a guarantee period of 15 (15 > 10) months results in more than 50% of the cars coming back for service under the guarantee.

It should now be clear 15 couldn't possibly be the correct answer.

You wrote:

"You want only 5% of the cars to fail or 95% not fail."

All the cars eventually fail. The question is when. We don't know when any one car will fail. We can only make inferences about when a proportion of the cars will fail.

Let x be a rv with distribution as described in the question. x denotes the number of months until a car fails. 95.15% of the area under the curve lies to the left of x=15. Therefore, in the first 15 months ~95% of the cars have failed and ~5% have not failed. A symmetry argument shows the correct answer to the problem to be 5.

I hope this is clear. I am open to being wrong and easily accept it when deonstrated.

Thank you for your time. Again, a reply is greatly appreciated.

Respectfully,

-Michael

[Lestat]

I'm following this thread, but staying out of it, because my math skills are terrible. I have to be in the exact right mood to figure stuff like this out, because I don't have the formal education. But...

<font color="blue">2) A mean failure time of 10 months suggests 50% the cars fail before 10 months and 50% the cars fail after 10 months (normal distribution -- median = mean). </font>

Are you sure this is what it means? To me, it means if I buy any given car out of 100 on the lot, I could "expect" it to last 10 months. And the difference (the times it will last longer or fail before 10 months), is the SD. I wouldn't "expect" every 2nd car I buy to NOT last 10 months or last longer than 10 months, even though I realize that it's unlikely to last "exactly" 10 months.

I'm sure I'm making a fool of myself, because you know much more about this than I do. I only know about SD as it pertains to my poker results. Every hour I play, I expect to earn my mean hourly rate, even though it's unlikely that I'll earn "exactly" my hourly rate in any given hour or series of hours.

And to the person who said, "First of all, it wouldn't make sense for a dealer to want the mayority of his cars (95%) to fail when the customers don't have the guarantee."

Of course it does! It COSTS dealers money to fix cars when they're still under warranty. They MAKE money fixing cars when they're out of warranty.

I know math problems in schoolbooks aren't always realistic, but instinct says that 5 months is too low. 15 months seems more appropriate. But that has nothing to do with the math and I haven't taken the time to work the problem out myself. That's just what my common sense would tell me.

[jogsxyz]

Dealerships want no cars to fail during the guarantee period. You buy an appliance. It's guaranteed for one year. It will fail at one year and one day.
The mean is ten months. Half the repairs will fail in less than ten months. No way does the repair shop wish to guarantee more than ten months. The answer must be less than ten months.
At a quick glance the answer should be four months, two standard deviations. In the real world the normal distribution only approximates the fail rate. Five months seems like a reasonable period for the guarantee.

[DiceyPlay]

You're not making a fool of yourself in my opinion.

Yes, I'm sure that's what it means. This particular dealer has observed that on average the cars they sell break down in 10 months. So the expectation for any car they sell from this point forward or until they recalculate their statistics is for that car to last 10 months before it needs a major service. An sd of three months means the standard deviation if 3 months. In a normal distribution 68% of the observations fall within 1 sd of the mean (average). An observation is noticing how long it took for a car they sold to require major service. So the dealer expects 68% of the cars they sell to require service anywhere from 7 to 13 months from the date of sale. 7 = 10 - 3 and 13 = 10 + 3. Likewise, in a normal distribution 95% of the observations fall within 2 sd's of the mean. So the dealer should expect 95% of the cars they sell to require major service between 4 and 16 months from the date of sale. 4 = 10 - 2 * 3 and 16 = 10 + 2 * 3.

I agree with you on your comment about what one of the other posters suggested.

Do you still think 15 months is more appropriate?

[Lestat]

I missed that it was a "used" car dealership! Sorry. So 15 months isn't what my instinct tells me anymore. -lol


<font color="blue">So the dealer should expect 95% of the cars they sell to require major service between 4 and 16 months from the date of sale. </font>

I agree. This seems right. But here's what's buggin me:

The mean is 10 and the dealer doesn't want to service more than 5% BEFORE the warranty expires. "Before" is the key word, because now you're only working with the TOP half of the bell curve, no? We can expect any given car to last 10 months. So how many MORE months are needed before we expect to be servicing greater than 5% of the cars we sell?

Seriously, I'm an idiot with math. This should be really simple for anyone that knows the calculations. DS, Bruce Z, Borodog, and many others could do this in their sleep. And no offense to madmak, yourself, and others who are probably just as capable. You guys could be right. If necessary, I can break out Malmuth's GTAOT and look up the correct calculations. But there are so many others on here who could do this off the top of their head. This is why I stay out of these threads, although I do find them interesting to read.

[BruceZ]

Of course you are correct, and the teacher should be ashamed to still have this wrong even after the error was pointed out to him.

The point at which 5% of the cars have failed occurs at approximately 1.64485 standard deviations before the mean, which is at about 5.065 months, so rounding off to an even 5 months will allow slightly less than 5% of the cars to fail within the warranty period, or specifically about 4.78% will fail in this period.

The student problem that he described is in no way the same problem because the students become less likely to fail as more time passes, whereas the cars are more likely to fail as more time passes.

It is also possible that he meant to ask now long the warranty should be so that 95% of the cars fail within the warranty period. This would explain his response, though it is not how warranties generally work.

[Lestat]

[ QUOTE ]
Of course you are correct, and the teacher should be ashamed to still have this wrong even after the error was pointed out to him.

The point at which 5% of the cars have failed occurs at approximately 1.64485 standard deviations before the mean, which is at about 5.065 months, so rounding off to an even 5 months will allow slightly less than 5% of the cars to fail within the warranty period, or specifically about 4.78% will fail in this period.

The student problem that he described is in no way the same problem because the students become less likely to fail as more time passes, whereas the cars are more likely to fail as more time passes.

It is also possible that he meant to ask now long the warranty should be so that 95% of the cars fail within the warranty period. This would explain his response, though it is not how warranties generally work.

[/ QUOTE ]

Dicey - You can rest assured this is right. I have "faith" this is right! /images/graemlins/grin.gif

[Silent A]

[ QUOTE ]
Of course you are correct, and the teacher should be ashamed to still have this wrong even after the error was pointed out to him.

The point at which 5% of the cars have failed occurs at approximately 1.64485 standard deviations before the mean, which is at about 5.065 months, so rounding off to an even 5 months will allow slightly less than 5% of the cars to fail within the warranty period, or specifically about 4.78% will fail in this period.

The student problem that he described is in no way the same problem because the students become less likely to fail as more time passes, whereas the cars are more likely to fail as more time passes.

It is also possible that he meant to ask now long the warranty should be so that 95% of the cars fail within the warranty period. This would explain his response, though it is not how warranties generally work.

[/ QUOTE ]

Quoted for its perfectly accurate correctitude.

BTW, I teach Hydrologic Engineering - a field that deals with lots of statistics - at one of the largest engineering faculties in North America.

Just to give weight to my qualifications.

[Hopey]

[ QUOTE ]
[ QUOTE ]
Of course you are correct, and the teacher should be ashamed to still have this wrong even after the error was pointed out to him.

The point at which 5% of the cars have failed occurs at approximately 1.64485 standard deviations before the mean, which is at about 5.065 months, so rounding off to an even 5 months will allow slightly less than 5% of the cars to fail within the warranty period, or specifically about 4.78% will fail in this period.

The student problem that he described is in no way the same problem because the students become less likely to fail as more time passes, whereas the cars are more likely to fail as more time passes.

It is also possible that he meant to ask now long the warranty should be so that 95% of the cars fail within the warranty period. This would explain his response, though it is not how warranties generally work.

[/ QUOTE ]

Quoted for its perfectly accurate correctitude.

[/ QUOTE ]

I remember running into teachers like this in high school. He'll refuse to admit he's wrong, even when the evidence piles up showing otherwise.

I'd be curious as to how many other students ended up with the same "wrong" answer of "5", and how many "correctly" answered "15".

[DiceyPlay]

My intention is not to get into a pissing match with him or her (I really don't know who the teacher is). The student simply wants the points they rightfully deserve and I told the student I would send an email.

Here is his reply:

Hello Michael,
Let me make the following assertions before getting into the problem again:

1) The "different problem" as you called it, statistically is identical to the original, so at least for my purposes it is not any different that the original.

2) From my point of view and many of my colleagues discussing similarities and dissimilarities is extremely helpful to make one understand an event, a problem or a procedure. This is not a fact but more of an observation, however, it has been proven in an educational environment over and over again.

Now regarding your email:

A) Your first claim about the intuition is correct, and your second statement is semi-correct. Hence your conclusion is flawed.

B) Your willingness to admit being wrong is noble but irrelevant to the problem. Also I was under the impression that we are trying to learn something here and not prove one another wrong. Even though at the end one solution is right and the other will be incorrect.

C) I tried to explain the problem in my previous email. Obviously, I have failed. Your desire and your drive as a tutor is commendable. But keep in mind that you may have some extra time on your hands, but I really do not have the time to discuss a problem that is about two months old and has no impact on the current materials in my class at this point.

You are more than welcome to stop by at my class about five to 10 minutes before it starts, and IF I have no other matters to attend to, I will be more than happy to go over the problem with you again.

Have a great weekend,

Kia

I'm sort of at my wits end on this. I think I'll email another teacher, but I'd rather not get anyone else involved as things can get unnecesarily ugly.

Oh well. I shouldn't have to work this hard when I'm not working!

Thanks to everyone for all your help. Thanks to Bruce for pointing out a major difference between the two problems.

[Silent A]

[ QUOTE ]
Thanks to Bruce for pointing out a major difference between the two problems.

[/ QUOTE ]

This is especially important. From what you have posted I'd be willing to bet that this teacher doesn't realize that the two problems are actually mirror images of each other. In fact, i'm willing to bet that the "analogy" (s)he made is the ONLY reason (s)he thinks (s)he's right.

If you're going to resolve this properly, you're going to need to point out this error.

[Hopey]

Wow...just as I suspected. The teacher is an insecure douchebag:

[ QUOTE ]
Your willingness to admit being wrong is noble but irrelevant to the problem. Also I was under the impression that we are trying to learn something here and not prove one another wrong.

[/ QUOTE ]

"You are obviously not as intelligent as I, so don't dare try to get me to admit that I'm wrong."

[ QUOTE ]
But keep in mind that you may have some extra time on your hands, but I really do not have the time to discuss a problem

[/ QUOTE ]

"I'm a busy man, and you're just a mere tutor. You obviously have time to waste, but as a ninth grade high school math teacher, I don't."

[ QUOTE ]
You are more than welcome to stop by at my class about five to 10 minutes before it starts, and IF I have no other matters to attend to, I will be more than happy to go over the problem with you again.


[/ QUOTE ]

"If you show up in my class, I'll claim to be too busy to talk to you."

[Hopey]

[ QUOTE ]
[ QUOTE ]
Thanks to Bruce for pointing out a major difference between the two problems.

[/ QUOTE ]

This is especially important. From what you have posted I'd be willing to bet that this teacher doesn't realize that the two problems are actually mirror images of each other. In fact, i'm willing to bet that the "analogy" (s)he made is the ONLY reason (s)he thinks (s)he's right.

If you're going to resolve this properly, you're going to need to point out this error.

[/ QUOTE ]

If he wants to resolve this properly, he needs to go over the teacher's head and email the head of the math department. This teacher has dug in his heels and has made it abundantly clear that he'll never admit that he's wrong.

[Victor]

you should go to the head of the dept. this teacher should be fired.

[Hopey]

[ QUOTE ]
this teacher should be fired.

[/ QUOTE ]

I wouldn't go that far...but he definitely needs to be brought down a peg...and the student should be given the mark(s) that he lost for getting that question "wrong".

[HeroInBlack]

Dear Dumb Bitch:

If 50% of the cars are going to come back within 10 months, how the [censored] are only 5% going to come back in 15 months?

Sincerely,
Dicey

[carlo]

Forward this post to the teacher. That oughta take care of it /images/graemlins/grin.gif.

[DiceyPlay]

Are we getting to the point of a pissing match?

Here is what I wrote back:

Hi Kia,

My intention is not to prove you wrong or to be right. I concede that being right is more pleasing than being wrong. But I've been wrong before and I'm sure I'll be wrong again. I am currently working on behalf of the student. Originally I told the student they should talk to the teacher about it. The next time I sat with the student they told me the teacher still said they were wrong. The student couldn't explain to me what the teacher said. I asked the student if they wanted the points and the student said yes. I told the student I would email the teacher. And now here we are - I'm spending much of my time writing emails about a problem that is not difficult or complicated. I received my B.S. in Statistics in 1993. I tutored my way through college. When I entered the professional work force I had 10 years of tutoring under my belt. I've worked as a Health Insurance Actuary and a Computer Programmer. I also concede that I have not had my head in statistics at his level since I graduated. How any of this is relevant to the problem at hand is beyond me, but maybe it will allow you to look more seriously at what I write.

If I'm wrong it should be a simple matter to demonstrate it to me.

As for differences between the problem on the Exam/Quiz and the one you used as explanation in your first reply - a significant difference is that as time marches forward students are more likely to pass whereas cars are more likely to fail. On that merit it seems obvious that the two problems are not "statistically" identical.

I don't consider myself an authority in Statistics. You, as a teacher at a community college, are obviously more educated than me. Is it within the realm of possibility that you might be wrong?

I'm simply trying to do the best that I can. Statistics is especially hard for many if not most students. A few points to a student might make the difference between one grade and another.

If I'm wrong I want to know about it. I want to know so that I can both learn and not make the same mistake in the future.

At this point I'm not sure what to do. I belive I've made a strong argument.

I apologize if my wording is rubbing you the wrong way. In person I'm a pleasant friendly person.

Best Regards,

-Michael

[Magic_Man]

[ QUOTE ]
[ QUOTE ]
this teacher should be fired.

[/ QUOTE ]

I wouldn't go that far...but he definitely needs to be brought down a peg...and the student should be given the mark(s) that he lost for getting that question "wrong".

[/ QUOTE ]

I disagree. Arrogant, ignorant teachers should be fired. This is yet another reason why I'm afraid to send my (future) children to school.

Anyway, the problem should be easy to solve. Here is the teacher's email:
[ QUOTE ]

Hello Michael,

Yes, at first glance 5 months seems like a correct answer. Actually when I did the problem first myself I got that answer!
But let me reword the problem.
Let's say that on average it takes 10 months for an average person to finish a training program and successfully pass a test, with SD of three months. If you want to make sure(guarantee) that 95% of the people enrolled will pass the test, how many months should the program last? You see 5 months does not make sense.

You want only 5% of the cars to fail or 95% not fail. If you set up the problem the way that you have, 95% of the cars fail and only 5% will not have problems.

Hope this helps,

Kia


[/ QUOTE ]

Here is what you should write:

[ QUOTE ]

The problem you have stated as analogy is in fact the opposite of the problem posed on the test. In your example, more students pass as time progresses. In the test question, more cars fail as time progresses. Since the owner wants to service as few cars as possible (5%) under the warranty, they need to be on the opposite tail of the curve.

Also, you are an arrogant ignorant bitch.


[/ QUOTE ]

You may want to leave out the last part.

~MagicMan

[Yads]

[ QUOTE ]
Dear Dumb Bitch:

If 50% of the cars are going to come back within 10 months, how the [censored] are only 5% going to come back in 15 months?

Sincerely,
Dicey

[/ QUOTE ]

[FortunaMaximus]

Entertaining thread. What a statistical improbability if she happens to drive a Kia. /images/graemlins/tongue.gif

What Lestat said, only I call it initution.

Heh.

[HeroInBlack]

Just to clarify one point, despite the name "Kia" and my reference to the teacher as a "dumb bitch," OP makes it clear the teacher is male.

He's still a dumb bitch.

[madnak]

[ QUOTE ]
you should go to the head of the dept. this teacher should be fired.

[/ QUOTE ]

[DiceyPlay]

He replied to my last with this:

Hello Michael,

I enjoyed reading your email so let me make this short and to the point:

1) It is neither your responsibility nor your place to act on behalf of a student specially when it comes to grading issues.

2) You are not one of my students so I neither have the obligation nor I want to "demonstrate" anything to you.

3) If the issue is about a) understanding or b) points or c) both, then it should had came out long time ago by the student.

4) I took you and your emails seriously and that is why I took my time and I responded to you. Please excuse my honesty here but your degree(s) and your work experience is irrelevant.

Thanks for all your email. This matter is closed as far as I am concerned, and no further communication is necessary.

Have a great weekend,

Kia

I wonder how many students will be penalized by his inaptitude and attitude before he stops teaching.

[madnak]

Out of line. Go over his head.

[Lestat]

I kinda knew it was coming to this. I sensed it from his first response and your 2nd email.

At least we're not talking about math anymore, so I can give my two cents.

It IS your business, because you are tutoring one of his students! You should copy Bruce Z's response and forward it to the school's principle. It's not bad enough this guy was wrong, but then he has an attitude on top of it! He doesn't sound like any teacher I'd want one of my kids to have. The school should know they what a moron they have on staff.

Sorry, I do get hung up on principle sometimes and if I were you, I wouldn't let it go until he apologizes to you and admits he's wrong! But that's me.

[surftheiop]

WTF?
I dont know anything about stats but this just sounds like someone who doesnt wanna admit he is wrong, even if he was right he is so arrogant i see no reason that he should be teaching.

[Iconoclastic]

I'd love to see his email to you after you get him fired for incompetency.

[Homer]

[ QUOTE ]
If 50% of the cars are going to come back within 10 months, how the [censored] are only 5% going to come back in 15 months?

[/ QUOTE ]

This says it all. Even someone with no mathematical background should know that the answer must be lower than 10 months. The teacher's responses are very saddening. Seems like the kind of teacher that wouldn't be willing to have an open dialogue in the classroom and thus would have no idea what his students need more help with.

[Hopey]

So are you going to go over his head? Please tell us you will. This guy's an idiot and shouldn't set foot anywhere near a classroom.

[Phil153]

HeroinBlack got it right.

[ QUOTE ]
Dear Learned Teacher:

If 50% of the cars are going to come back within 10 months, how the [censored] are only 5% going to come back in 15 months?

If I don't receive a revocation of this grade and an immediate unconditional apology to both me and the student, admitting your error, I'm reporting you to the faculty for your unprofessional attitude and obvious unfitness for your job.

Have a nice day.
Dicey

[/ QUOTE ]

You were way too nice, and long winded.

[flatline]

[ QUOTE ]
So are you going to go over his head? Please tell us you will. This guy's an idiot and shouldn't set foot anywhere near a classroom.

[/ QUOTE ]

Totally agree. Plus it would provide sweet drama.

[DiceyPlay]

Yes I did email the Dean of Mathematics and CC'd my Boss. But I fear that I've somehow done something wrong. I don't want to be viewed as a troublemaker. I hope institutional education politics aren't like corporate politics - I fear they are.

But this situation needs to be exposed, no?

[Hopey]

[ QUOTE ]
Yes I did email the Dean of Mathematics and CC'd my Boss. But I fear that I've somehow done something wrong. I don't want to be viewed as a troublemaker. I hope institutional education politics aren't like corporate politics - I fear they are.

But this situation needs to be exposed, no?

[/ QUOTE ]

If only because the teacher was a douche to you, yes.

[Colima420]

[ QUOTE ]
I think that the professor made a typo and the problem should have been stated as:

"A used car dealership has found the length of time before a major repair is required on the cars it sells is normally distributed with mean equal to 10 months and standard deviation of 3 months. If the dealer wants only 5% of the cars to fail AFTER the end of the guarantee period, how many months should the car guarantee be? "

First of all, it wouldn't make sense for a dealer to want the mayority of his cars (95%) to fail when the customers don't have the guarantee. It only makes sense for the dealer to want only 5% of cars to fail after the guarantee. This way the guarantee actually works. If 95% of cars need repairs after the guarantee is over, then the guarantee has no purpose.

Secondly, if we analyze his example of his reply to you (regarding the time it takes a person to complete a course), it is almost identical to the car problem with the AFTER word in it.

This way,


z = (x - mu) / sigma

The z critical value for .05 (probability of car failure, since he wants 5%) is 1.645. This can be found in any z table.

now if we solve the previous equation with this number we get:

1.645 = (x - 10) / 3
4.935 = x - 10
14.935 = x Rounding up we get x = 15. We need to have the guarantee to be for 15 months in order to have 5% of all cars fail after that.

So my whole theory is that the original problem should have been: "How many months should the guaranteee be in order to have 5% of the cars not be covered by it?"

or conversely: "How many months should the guarantee be for in order to have 95% of the cars covered by it"?

Colima420

[/ QUOTE ]


Sorry. I was tired/drunk when I first responded to this.

The answer is definitely 5 months.

z critical value for .05 is -1.645.

z = (x - mu) / sigma

-1.645 = (x - 10) / 3

-4.935 = x - 10
5.065 = x

If the guarantee is for 5 months, the dealership will only have to cover 5% of the cars under the warranty.

I would erase my first response, but I can't.

PS. The teacher is an ass.

Colima420

[CORed]

Forward all the emails to his department head. This professor should be fired. He is clearly unqualified.

[Jasper109]

I teach this concept in grade 12 high school Math, and have used virtually identical questions on tests.

You are right, he/she is an ignoramus. I applaud you in terms of what you have done so far. Don't back down.

[Aleo]

You have been far too diplomatic about this whole situation, and honestly, that may be a significant part of the problem.

[Phil153]

[ QUOTE ]
You have been far too diplomatic about this whole situation, and honestly, that may be a significant part of the problem.

[/ QUOTE ]

Now you're being too diplomatic. He comes across in those emails as an overly apologetic, long winded pussy. Some people (like the professor, it seems) are stupid, and take timidness as a sign that you're weak or wrong.

I agree that OP probably was part of the problem. But the lecturer's attitude and incompetence still needs to be brought to the attention of someone in charge.

[_brady_]

[ QUOTE ]
You want only 5% of the cars to fail or 95% not fail. If you set up the problem the way that you have, 95% of the cars fail and only 5% will not have problems.

Hope this helps,

Kia

[/ QUOTE ]


What the hell? Someone who makes a statement like this should not be teaching statistics. It doesn't take someone with a PhD in statistics to know that as time goes on more cars fail. His statement says that as time goes on cars "fix" themselves and we have less failed cars.

Let's take the inverse of his answer. Let's say the mean fail time is 10 months, SD is 3 months, and we want to find how many cars fail before 15 months.

z=(x-mu)/sigma

z=(10-5)/3

z=1.6667

Using a z-table we find z=1.66 corresponds to .9515

Therefore 95.15% of cars fail before 15 months as everyone else has stated in this thread.

Now let's look at the original question:

If the dealer wants only 5% of the cars to fail before the end of the guarantee period, how many months should the car guarantee be?

All I have to say is...LOL.

[Hopey]

I sure hope the OP lets us know what the Dean has to say...

[DiceyPlay]

Here is what I emailed the Dean of Mathematics:

Here is a copy of the instructors reply to my last. I will not pursue this issue any further. I apologize if I've done something wrong. And I apologize if I've inconvenienced either of you.

--------------------------------------------------------------

Hello Michael,

I enjoyed reading your email so let me make this short and to the point:

1) It is neither your responsibility nor your place to act on behalf of a student specially when it comes to grading issues.

2) You are not one of my students so I neither have the obligation nor I want to "demonstrate" anything to you.

3) If the issue is about a) understanding or b) points or c) both, then it should had came out long time ago by the student.

4) I took you and your emails seriously and that is why I took my time and I responded to you. Please excuse my honesty here but your degree(s) and your work experience is irrelevant.

Thanks for all your email. This matter is closed as far as I am concerned, and no further communication is necessary.

Have a great weekend,

Kia

--------------------------------------------------------------

I don't see this as a grading issue. To me a grading issue would be how to incorporate the tests into a final grade or how much partial credit to give on a problem or whether or not to give points for homework and/or attendance. Grading issues, to me, are not black and white - they are subjective and are argued on the basis of fairness. This is a case of grading error - this is black and white.

Teachers have power over students. Considering this teachers stance with regard to our email communications it's hard to imagine he is having any kind of open dialogue in his classroom and thus he would have no idea what his students need more help with. That is saddening. If he can stand his ground as he has in our communications imagine how he is with students who are, almost without exception, ill-equipped to argue mathematically. When teachers conduct themselves as this teacher appears to be students are unfairly punished. I wonder how many students have been and will be penalized by the actions of this teacher.

I don't want to be viewed as a troublemaker. But this issue seems to hit somewhere near the heart of education. I suspect you and MKC have your plates full of higher profile, if not more important, issues. I sincerely believe that I provide service to the students as a tutor and am of value to the students, the school, and educational mathematics.

Best Regards,

-Michael

Special thanks to BruceZ and Homer. I used some of what each of you had to say in my emails. Thanks to all who have chimed in and helped me to understand this frustrating situation.

[Hopey]

Did you include the original "warranty problem" in your email to the dean? The fact that the teacher is a douche is a major issue...the fact that he's a douche who wasn't able to understand the solution to the "warranty problem" is what should get him in trouble.

To put it another way, there are plenty of teachers who are douches...but as long as they know the material, the students can still benefit. A teacher who is a douche and doesn't understand the material is of no benefit to anyone.

[tshort]

Dicey,

While you are most definitely correct that, as worded, the answer is 5 months and not 15 months, I think you have over-stretched your bounds as a tutor in this entire situation.

The student should have first brought the issue to his teacher. "Hey I reviewed this problem with my tutor... "

Then, you might be able to e-mail the professor and ask her to take the time to review the problem as worded or consult a second opinion, for the sake of the student you are tutoring.

This should have been the student's initiative. As played, the teacher is a douche and is wrong. The fact that the teacher still hasn't come to realize this is ridiculous.

I'm anxious to read more of the OOT-style drama bomb that is ensuing.

[paperjam]

Dicey,

I have to admit, I am impressed with your maturity in your communications with this professor. You are correct and he is making incorrect claims, non-parallel comparisons, and ad hominem arguments.
E-mails the Dean was an ok move, however, I think what should be done is that you should have a number of math professors/tutors/educated people independently work through the problem. Then, when all 10 of them give you the answer as 5 months, submit that to the head of the math department. I don't remember if by dean you mean of the math dept. or the school, but the head professor is the person to go to.
At the very least, if the questions intent was to arrive at the 15 month answer, then is was extremely poorly worded, in which case, the professor should be willing to admit it was a bad question and accept the student's answer as correct.
Posts like this make me really angry, just because I want resolution - I want the person who is in the right to win. Don't fail me! But keep being mature about it as you have been and don't resort to any ad hominem type arguments.

[Hopey]

Any update to this?

[toybux]

Man, this professor sounds like he/she will end up at a community college someday. Professors like this tend to get run out of 4-year schools fairly quickly when someone catches on that they don't really know what they are talking about. This professor might just lack reading comprehension, though. I'd be interested in hearing what happened here.

[DiceyPlay]

I didn't get a response from the dean. My immediate supervisor who was cc'd on the emails I sent to the dean wrote to me with this and cc'd the problem professor and somebody I don't recognize:

___________________________
Dear Micheal,

While I understand you wanting to help your student, it is very clear in our Tutor Handbook that it is our policy that tutors do not intervene in matters between students and instructors. If the student is unhappy about the scoring of an exam or grade in a course, the student should be empowered to take it upon himself/herself to discuss the matter with the instructor. If dissatisfied with the response, the student can follow up with a visit to the Dean. However, grading issues are usually left to the discretion of the instructor. If you have questions or problems, please come address them with me first.
___________________________


Now I don't know what to do or if it's worth it to do anything. I don't even know if the dean has thought through the problem and sees the teachers incompetence. If I continue to pursue the issue I think I will be let go. They seem to be focusing more on my break of policy and procedure than the teachers incompetence. My break of policy and procedure is definitely wrong. But my break was innocent and it uncovered a situation that should be addressed. The ends don't justify the means but unjust means don't invalidate the ends either specially when the means were done innocently. It's aggravating to think about - so I try to just not think about it.

Thanks for all the input!

-Michael

[srjunkacct]

[semi-grunch]

Dicey, you really have no business confronting the professor or Dean (even though your answer is correct). If your student wants to press the issue, then by all means help him/her prepare a complaint and send it to the Dean. Finding other students who were similarly penalized and filing a collective complaint would probably be even more effective.

If the student doesn't wish to press the issue directly, then you really should stay out of it.