A Probability Question

Technochicken

Technochicken

Posts: 716   +2
I had this math problem on a test today:

The average GPA at a school is 3.4, with a standard deviation of 0.2. What is the probability that your GPA is lower than 3.7, given that your GPA is higher than 3.3(supposing your gpa can be between plus infinite and minus infinite.)

I found the answer like this:

(Probability(gpa>3.3) and (gpa<3.7)) / Probability(gpa>3.3)

By this, you get about .9033

My friend did this problem a different way, which takes a little explaining:

The probability that you score higher than 3.3 is 1, because it is given that you score above that. So logically, the probability that you score between 3.3 and 3.7 is 1- the probability of a gpa>3.7.

But when you calculate this, you get .933, which is the wrong answer.

My friend and I can't figure out why his way doesn't work. Any ideas?
 
You're really reading too much into my post. Have fun with the math, but shooting for a 4.0 is still sound advice.
 
My daughter recently took a tour of a great pharmacy school in our area and they informed us that the "average" GPA for accepted candidates is 4.0! How do you get an "average" of 4.0 unless all candidates are 4.0? I am guessing that some high schools give you extra credit or something so that you can get a 4.1 or higher? Sort of like an A+? I remain mystified by that statement and this thread reminded me about it.
 
I was just reading about a college, and in the back of the pamphlet, it said the average gpa was 4.3. I think AP classes in addition to all A's can put your gpa past 4.0.
 
You are right, Techno. I just did a little research on this and it appears that many high schools use a "weighted" gpa (colleges do not and it is not possible to score higher than a 4.0 at the college level.) This weighted gpa takes into account any advanced placement courses and, for those courses, the student can earn up to a 5.0. So, it would be theoretically possibler to earn a 5.0 if all you did was take all AP courses in high school and aced them all. Whew.

And pity the poor student who does not take any AP courses, gets straight A's and gets the lowly 4.0 gpa that is only "average" in some places.
 
Hope this helps ...

Assuming normality (question cannot be answered without it) ...

First standardize the values given like so:

z = (x - mu) / sigma
= (3.3 - 3.4) / 0.2
= -0.1 / 0.2
= -0.5 -----------> z-value corresponding to a GPA of 3.3

z = (3.7 - 3.4) / 0.2
= 0.3 / 0.2
= 1.5 ------------> z-value corresponding to a GPA of 3.7


Now you want the probability that it's between those two GPA values (this is the value for AND)

On the normal curve, this is the value between 3.3 (-0.5) and 3.7 (1.5) ... which corresponding to the tables gives you a value of (0.43319 + 0.19146) = 0.6247 ....

Probability that GPA > 3.3 = 1- (0.5 - 0.19146) = 0.69146

That's where you get the 0.6247 / 0.69146 = 0.9033.

Now, as for your question about your friend's answer:

P(A) = probability that you get less than a GPA of 3.7
P(B) = probability that you get more than a GPA of 3.3

P(A/B) = P(A AND B) / P(B) (Formula for conditional probability for DEPENDENT events) ...

By assuming that P(B) = 1, we get that P(A/B) = P(A AND B) = P(A) = 0.93319 (the value he got) ....

Now, P(A/B) = P(A) is the formula for conditional probability based on INDEPENDENT events. Therefore he's made the assumption that they are independent when they are clearly not... Lets say you have a GPA of 3.5 - it was still DEPENDENT on the fact that it was above 3.3 ....

Moral - you cannot assume independence until you prove it. A and B are Dependent events and thus your answer is correct and his is wrong.

Spyder_1386 :)
 
Full Quote

bobcat said:
42.7 percent of all statistics are made up on the spot. ;)
Click to expand...
captaincranky said:
I hope you didn't just make that up,
Click to expand...
hellokitty[hk] said:
I don't think thats a statistic, either way, its a joke, it isn't supposed to be true, its supposed to be funny...lol
Click to expand...
The captain & hellokitty[hk] (as one would expect from a fellow cat) got it right! :)
For the sake of those who didn’t, I restate my quote more fully:

42.7 percent of all statistics are made up on the spot, just like this one. (bobcat)

As regards the reliability of stats, there is a more famous quote, unfortunately not by bobcat:

There are lies, damn lies and statistics. (Benjamin Disraeli)
 
The captain & hellokitty[hk] (as one would expect from a fellow cat) got it right!
Click to expand...
my signature (I actually saw this somewhere else, and decided it was worth stealing)..."People are imbeciles, lucky thing god made cats."
 
Cat Quote

On another board, where I was also connected to a cat, I was using as sig my own quote:

A cat is clever, clean, cool, quiet, cute, cuddly. (alias bobcat)
 
NetCablesPlus said:
You are right, Techno. I just did a little research on this and it appears that many high schools use a "weighted" gpa (colleges do not and it is not possible to score higher than a 4.0 at the college level.) This weighted gpa takes into account any advanced placement courses and, for those courses, the student can earn up to a 5.0. So, it would be theoretically possibler to earn a 5.0 if all you did was take all AP courses in high school and aced them all. Whew.

And pity the poor student who does not take any AP courses, gets straight A's and gets the lowly 4.0 gpa that is only "average" in some places.
Click to expand...

So, does that make 4.0 all "B"s then.
 
I know how to change an F into a B with a fine point pen because your mom made you take home ec and sew a dress and make quiche when the fellas were in metal shop making really cool tool boxes!!......umm....very interesting Techno.
 
I used to be a mailman. Report card day was always such a gas. I loved to revel in shattering lives, causing little bottoms to be thrashed, and separating students from their pompous illusions of knowing it all, in general just making great things happen all around town.
 
"its a little known fact....."

captaincranky said:
I used to be a mailman. Report card day was always such a gas. I loved to revel in shattering lives, causing little bottoms to be thrashed, and separating students from their pompous illusions of knowing it all, in general just making great things happen all around town.
Click to expand...


Sarcastic positivity! :haha::haha:
 
NetCablesPlus said:
My daughter recently took a tour of a great pharmacy school in our area and they informed us that the "average" GPA for accepted candidates is 4.0! How do you get an "average" of 4.0 unless all candidates are 4.0? I am guessing that some high schools give you extra credit or something so that you can get a 4.1 or higher? Sort of like an A+? I remain mystified by that statement and this thread reminded me about it.
Click to expand...
Can't crush the little kiddies emotions now. Everyone gets an "A". Libs always fail to teach kids reality. In reality people fail, don't get promoted, get passed over, lose at sports, etc....

Can't play tag any more either because someone will be "it".
 
Yeh that above a 4.0 stuff is pretty lame. Back in my day it didn't matter if you took hard classes or easy classes, whatever grade you got factored into your GPA equally. Now stuff is weighted and apparently given values above a 4.0 on a 4.0 scale. Kids need to learn failure and hard work, and sometimes even failure despite hard work.
 
Yeh that above a 4.0 stuff is pretty lame. Back in my day it didn't matter if you took hard classes or easy classes, whatever grade you got factored into your GPA equally. Now stuff is weighted and apparently given values above a 4.0 on a 4.0 scale. Kids need to learn failure and hard work, and sometimes even failure despite hard work.
Click to expand...
Maybe, but then again, when was the last time you have taken an easy class compared to a hard AP class? Oh and you do have to take the AP test too, I don't know maybe they give you some extra stuff for the tests.
 
heh. hellokitty[hk], I took the most advanced classes my little high school offered (except English IV) and I still entered my university with a far below average knowledge (people already had calc and chem and physics - I didn't). And now... I have a BS in Geology & Geophysics with an emphasis area of Groundwater and Environmental Geochemistry, a Masters of Science in Engineering Management, and I'm 1 year into a PhD program in Geology, with my dissertation being on Shallow Depth Carbon Dioxide Sequestration.

And I have failed, quite a bit in trying to get this far. I had to drop Chem 1 twice, then I took it at another college over the summer only to get an A and find out it wouldn't transfer to my college. So I took it a 3rd time (here) and 4th time total and got a C. Then I took its successor class, and also got a C. I also got a D in Calc 1 here, took Calc 2 at another college and got a B. So I fully stand by my statement on how it is good sometimes to experience failure even when you are trying not to fail.

And also, to give a non specific answer to your question. Those weighted GPA's and/or classes don't mean anything in college, in college you can take 3 hours of Art Appreciation and 3 hours of Quantum Physics and they count exactly the same towards your GPA. So why make it different for HS?
 
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