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?

Bust your a** for a 4.0, and you won't have to worry about that s***.

It's not **** to me. I actually enjoy math, especially probability.

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

xchgfsdhgfnhgnhb

yeah, Advanced Placement Courses.

one of my friends has a 4.7

42.7 percent of all statistics are made up on the spot.

I hope you didn't just make that up,

hoefully your not talking about me,

im still in highschool.

i would know,

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

Full Quote

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)

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)

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.