Post by: fleet street on August 31, 2013, 05:56:55 pm
Example Question:
Spoiler
If X is a binomial random variable with parameters n=20 and p=0.3, then the mean and variance of X are closest to:
A.
B.
C.
D.
E.
A.
B.
C.
D.
E.
Spoiler
Incorrect Responses
B: Incorrect assumption that
C: The values of
D: Incorrect assumption that
E:
Because of the nature of this SAC, there are few multiple choice questions which provide detailed solutions in this format.
I have a few questions that I would like help trying to discover what the multiple choices are supposed to represent.
Also, I would be happy to try to help anyone else doing a SAC like this if you post your question. :)
The question that I need help with is attached. Specifically, I need help with A,B and C. (The answer is D and I have already worked out the error in E.)
Thanks for following this post! I know that I haven't written it so that it is easily understandable :P
Post by: TrueTears on September 02, 2013, 06:16:09 pm
Post by: fleet street on September 02, 2013, 08:12:53 pm
Post by: psyxwar on September 02, 2013, 08:14:54 pm
Thanks! But what I'm trying to get at is: "Why would someone put 0<q<0.4?"Nossal offers methods in yr10? :(
Post by: TrueTears on September 02, 2013, 08:21:06 pm
Thanks! But what I'm trying to get at is: "Why would someone put 0<q<0.4?"I don't understand. 0<q<0.4 is incorrect.
Post by: fleet street on September 02, 2013, 09:00:18 pm
I don't understand. 0<q<0.4 is incorrect.I know. I need to know how someone, using faulty reasoning, would get that answer. Please see the example question that I have given (in spoilers) to see what I'm looking for.
Nossal offers methods in yr10? :(Kind of. I've been accepted to do it early, but it isn't usually offered. About 10 other kids do languages 3/4 in year 10.
Post by: TrueTears on September 02, 2013, 09:23:10 pm
I know. I need to know how someone, using faulty reasoning, would get that answer. Please see the example question that I have given (in spoilers) to see what I'm looking for.I use correct reasoning.
Post by: fleet street on September 02, 2013, 09:32:19 pm
I use correct reasoning.:D Good point! I'm kind of annoyed at this SAC too.
Post by: BubbleWrapMan on September 02, 2013, 09:39:11 pm
I know. I need to know how someone, using faulty reasoning, would get that answer.Although thinking about this is good, you're not always going to be able to determine how the incorrect answers were generated, since they might have just been thought of on the spot without much thought other than "it looks sort of correct".
Perhaps more interesting is to consider that you can eliminate A, B, and C just by looking at all the options. There is only one correct answer, but if A is true then D is also true by transitivity (i.e. if q = 0.4 then 0 < q < 0.8 also holds). Option A being correct means there are two correct answers, which can't happen, so A must be false.
If B is true, then D is also true by similar argument, so B being true leads to two correct answers. Hence B is false.
If C is true, then B and D are also true. Hence C is false.
Post by: Planck's constant on September 02, 2013, 09:57:45 pm
I need to know how someone, using faulty reasoning, would get that answer.
Get real, my friend.
TrueTears has not used faulty reasoning in maths since he was 3-months old
Post by: fleet street on September 02, 2013, 10:18:18 pm
Although thinking about this is good, you're not always going to be able to determine how the incorrect answers were generated, since they might have just been thought of on the spot without much thought other than "it looks sort of correct".Good point, I'll keep this in mind. Also, your argument is interesting.
Perhaps more interesting is to consider that you can eliminate A, B, and C just by looking at all the options. There is only one correct answer, but if A is true then D is also true by transitivity (i.e. if q = 0.4 then 0 < q < 0.8 also holds). Option A being correct means there are two correct answers, which can't happen, so A must be false.
If B is true, then D is also true by similar argument, so B being true leads to two correct answers. Hence B is false.
If C is true, then B and D are also true. Hence C is false.
Speaking of faulty reasoning, any mistake here? :P
Get real, my friend.
TrueTears has not used faulty reasoning in maths since he was 3-months old
(https://upload.wikimedia.org/math/3/1/4/31446199677b3c212c5ebe092f035e06.png)