Post by: luken93 on October 31, 2011, 05:56:30 pm
I'm assuming this is right, but feel free to pick me up on anything I've missed:
Normal Distribution
The range of scores on a particular test are such that they hold a mean of 60 with a standard deviation of 4.
NORMAL CDF
a) Find the probability of a student's scores lie between 55 and 62
On the TI-Nspire;
On the classpad;
On paper:
Let X be the range of scores of students on the test.
NORMAL PDF
b) Find the probability that a student's score is 61
On the calculator;
On paper:
Let X be the range of scores of students on the test.
INVERSE NORMAL
c) 75% of students passed the test. Find the score needed to pass the test.
On the calculator;
On paper:
Let X be the range of scores of students on the test.
Let a be the minimum value needed to pass, Find a such that
Therefore a score of 57.3020 is needed to pass.
Binomial Distribution
BinomPDF
d) The probability that a particular student passes the test is 0.4.
i) If this student sits 3 tests that are independent to the other, what is the probability that the student passes 2 out of 3 tests.
On the calculator;
On paper:
Let Y be the performance of the student in the 3 tests
BinomCDF
ii) This particular student needs to pass at least one of the tests to make his parents happy. What is the probability that his parents will be happy?
On the calculator;
On paper:
Let Y be the performance of the student in the 3 tests
Number of Trials
iii) The student is now getting very worried about his parents. To ensure that the probability that his parents are happy is 0.95, how many tests will he have to sit if he has to pass at least one of them?
On paper:
Let Y be the performance of the student in the m number of tests
Find m such that
Hopefully that's all correct!
Post by: REBORN on October 31, 2011, 05:57:37 pm
Is there meant to be a symbol in b/w?
Post by: gossamer on October 31, 2011, 06:00:05 pm
Post by: b^3 on October 31, 2011, 06:01:04 pm
Use \sim in LaTeX and it will work.
Post by: david10d on October 31, 2011, 06:01:46 pm
bad habit using calculator syntax :P
Post by: nacho on October 31, 2011, 06:04:04 pm
(Let X = number of ..)
Post by: Asx4Life on October 31, 2011, 08:40:09 pm
How about the question where it asks for find the minimum number of trials...
How do we give notation for that?
Post by: tony3272 on October 31, 2011, 08:51:33 pm
Post by: tony3272 on October 31, 2011, 09:02:11 pm
Post by: luken93 on October 31, 2011, 09:05:30 pm
Post by: Asx4Life on October 31, 2011, 11:14:03 pm
How about the question where it asks for find the minimum number of trials...
How do we give notation for that?
Anyone can answer this? ;) Thanks
Post by: nacho on October 31, 2011, 11:17:36 pm
have not ever seen vcaa complaining about it
Post by: luken93 on October 31, 2011, 11:37:13 pm
Does that answer your question?How about the question where it asks for find the minimum number of trials...
How do we give notation for that?
Anyone can answer this? ;) Thanks
Post by: abeybaby on November 01, 2011, 12:00:43 am
Hmmm. As much as I agree with you tony, I dunno if it's really necessary. Can we get any clarification on this though? I don't want to give any false advice!
yeah, luken is right... plus the last line should read Pr(1≤Y≤3), not Pr(1<Y<3).
Post by: abeybaby on November 01, 2011, 12:03:13 am
Theres an answer up there. You really only need to get to the 5th line, then go straight to the answer..
for the solving for n stuff..
Post by: Greatness on November 01, 2011, 01:21:48 pm
Post by: luken93 on November 01, 2011, 01:26:30 pm
Would VCAA give us a solve for n question on exam 1? - The calculations would have to pretty simple tho...Yeah I would doubt it, but if they did I can't imagine it being more than a Pr(X >= 1) = ...., to keep the calcs relatively simple..
Post by: tony3272 on November 01, 2011, 01:45:08 pm
Post by: yabbaboo on November 05, 2011, 06:13:37 pm
Post by: b^3 on November 05, 2011, 06:22:02 pm
Um, are we allowed to write this whole thing down on the paper, eg normcdf(60, 95, 60, 15)? I always wrote like that on my sacs and I never lost marks for that.Thats calculator syntax, I don't think you would lose marks for writing it, you just wouldn't get the marks for writing the X~(60,0.2). VCAA are always stating in the assesment reports to not write caclulator syntax.
Remember that with sacs, your teachers may be marking a slightly different way to VCAA.
Just a quesition guys, what do we write when we have the inversnorm function?
i.e. Binomial X~(n,p)
Normal distributions X~(u,o^2)
inversnor X~"_"(u,o^2)
Post by: mjwalka on November 05, 2011, 10:24:14 pm
Post by: b^3 on November 05, 2011, 10:33:47 pm
Post by: AleksIlia on November 05, 2011, 10:50:01 pm
Post by: Greatness on November 05, 2011, 10:58:07 pm
You have to remember that the normal bell curve extends to infinity.
Post by: AleksIlia on November 05, 2011, 11:07:49 pm
if you want Pr(X>2) then you're going from 2 to inf which is why there is the upper and lower for CDF but if you want it for a particular value you just use PDF.
You have to remember that the normal bell curve extends to infinity.
But how do you find Pr(X=2) for a normal distribution if Pr(X=x) is 0 for a specific value of x
Post by: b^3 on November 05, 2011, 11:10:14 pm
Post by: AleksIlia on November 05, 2011, 11:19:45 pm
Post by: b^3 on November 05, 2011, 11:22:55 pm
Oh, I see then, but if I put in the normal distribution mean 0 sd 1 for x value of 0 I don't get 0.5?Wait, you're right I may be wrong let me just check.
Post by: b^3 on November 05, 2011, 11:31:20 pm
Sorry for the confusion.
EDIT: sometimes we get a question like the example in the first post, test scores (where you can't have half a mark) so this will allow you to calculate the probability of say 65 /100 or 69/100.
Post by: AleksIlia on November 05, 2011, 11:35:59 pm
Post by: b^3 on November 05, 2011, 11:38:10 pm
Okay thanks! Also thanks for those CAS guides, super helpful. Good luck Tuesday :)No problem, but remember luken93 is the one who knows what hes doing when it comes to probability. Anyway good luck for the next weeks of exams.
Post by: luken93 on November 06, 2011, 02:56:05 pm
Hahaha cheers.Okay thanks! Also thanks for those CAS guides, super helpful. Good luck Tuesday :)No problem, but remember luken93 is the one who knows what hes doing when it comes to probability. Anyway good luck for the next weeks of exams.
However, does anyone know of a nice way to present your working for steady state?
Is it sufficient just to say that Pr(A long term) = b/(a + b) according to your transition matrix orrr?
Post by: paulsterio on November 06, 2011, 04:47:32 pm
On the nSpire, I believe it is normCDF(lower, upper, mean, standard deviation)
On the ClassPad, however, it is normCDF(lower, upper, standard deviation, mean)
you might like to include that on your guide just for clarity