Normal Distributions

[costargh]

Ok, so we can presume that VCAA's method is the one most applicable here yeh?

So, 5.5% corresponds to a SS of around 42 you would think?

[Collin Li]

Why are you using an exam mark to figure that out? Just use the scaling reports. They tell you the mean and standard deviation (usually around 30 and 7 respectively), which makes it fairly easy to calculate.

A study score of 42 should be approximately the top 4.1% of students in the subject.

[Mao]

i think he's trying to predict his SS from his exam score


coblin: are you sure that's VCAA's method? by that, about 2.98% of people achieve full score [or more], and 2.60% of people get 182? =\

The normal distribution is definitely truncated: http://en.wikipedia.org/wiki/Truncated_normal_distribution

the probability density function of a truncated distribution [from wikipedia]:





hence, the cumulative function would be:



tada~ conditional probability~

[Mao]

For the sake of clarity, my method (conditional probability) [with suggestion from caramel to implement each discrete data range to be from -0.5 to +0.5]:

for discrete set of data

that gives:
0 - 100%
25 - 95.6%
50 - 85.2%
75 - 67.5%
100 - 44.9%
110 - 35.8%
120 - 27.4%
130 - 20.0%
140 - 13.7%
150 - 8.70%
160 - 4.87%
162 - 4.23%
164 - 3.64%
166 - 3.08%
168 - 2.56%
170 - 2.08%
172 - 1.63%
174 - 1.22%
176 - 0.83%
178 - 0.48%
and finally for amusement:
180 - 0.15%

[costargh]

Thanks Mao, but then why would VCAA do it such that the top 10 % is 152 or above. Why would they use that way of calculating the distribution if according to their data, people get above the total marks allocated for the exam. lol

This is really annoying lol. Thanks for the effort guys

Finally, with a score of 83/90 (ie. half way between cut off A+ and maximum mark allocation) (where cut off A+ is 76/90 and max score is 90/90), would anyone like to predict mathematically what study score I would be looking at if I did proportionately well on exam 2 (ie. disregard the score on the exam and just take into account the percentile rank)

[Mao]

Why would they use that way of calculating the distribution if according to their data, people get above the total marks allocated for the exam. lol

I do not believe that's what happens. I think the bell curve is truncated at 0,180 (I defined it to be -0.5 to 180.5 since 0 and 180 are valid scores)

as for what VCAA actually do in detail, I am unsure. But I am do think that their model does not include people with unrealistic scores (well, I hope at least)

[costargh]

Hmm VCAA is confusing

Finally, with a score of 83/90 (ie. half way between cut off A+ and maximum mark allocation) (where cut off A+ is 76/90 and max score is 90/90), would anyone like to predict mathematically what study score I would be looking at if I did proportionately well on exam 2 (ie. disregard the score on the exam and just take into account the percentile rank)

Just incase I edited while you were replying and missed this. Lol don't feel obliged, just pointing it out

[Collin Li]

Mao, if you calculate it, you will get 10% for an upper bound of infinite, and 7.8% for an upper bound of 180 (lower bound being 152).