Calculator Free Question

[nerd]

This is from the Australian Education Academy 2006 Methods Paper: Examination 1.

Question 1

I found the E(X) of a certain prob distribution to be 2.12, which is correct. It then asks me to find the Var(X) and sd(X). Firstly, are we excepted to be able to evaluate by hand? And even worse, how is one supposed to evaluate for the standard dev? I CAN'T DO THAT WITHOUT A CALULATOR!!!

Question 2

The hight of a certain population of adult males is normally districtuber with mean 174 cm and standard dev of 8 cm.
a) Find the probability that the height of a randomly selected individual will exceed 190 cm.

How do you do this without a calculator?

[shinny]

Overall, it just seems like AEA (who the hell are they anyway?) forgot to cater for the course change. Prior to 2006, exam 1 was calc-active so yeh.

[Collin Li]

Question 1

I found the E(X) of a certain prob distribution to be 2.12, which is correct. It then asks me to find the Var(X) and sd(X). Firstly, are we excepted to be able to evaluate by hand? And even worse, how is one supposed to evaluate for the standard dev? I CAN'T DO THAT WITHOUT A CALULATOR!!!

Weak.

Just kidding

Question 2

The hight of a certain population of adult males is normally districtuber with mean 174 cm and standard dev of 8 cm.
a) Find the probability that the height of a randomly selected individual will exceed 190 cm.

How do you do this without a calculator?

You can do this if you make some approximations. You know that two standard deviations from the mean is approximately 95% right? Use that fact. I'm not sure whether the course assumes that knowledge, or whether the exam paper will actually say something like: "you may assume that the probability of being within 2 standard deviations of the mean is 95%"

The answer should be 0.025

[excal]

Question 1

I found the E(X) of a certain prob distribution to be 2.12, which is correct. It then asks me to find the Var(X) and sd(X). Firstly, are we excepted to be able to evaluate by hand? And even worse, how is one supposed to evaluate for the standard dev? I CAN'T DO THAT WITHOUT A CALULATOR!!!

Weak.

Just kidding

Question 2

The hight of a certain population of adult males is normally districtuber with mean 174 cm and standard dev of 8 cm.
a) Find the probability that the height of a randomly selected individual will exceed 190 cm.

How do you do this without a calculator?

You can do this if you make some approximations. You know that two standard deviations from the mean is approximately 95% right? Use that fact. I'm not sure whether the course assumes that knowledge, or whether the exam paper will actually say something like: "you may assume that the probability of being within 2 standard deviations of the mean is 95%"

The answer should be 0.025

Yes, they do. The 68% - 95% - 99.7% (empirical) rule I've seen in MM textbooks,

[doboman]

yeah thats in the course

[excal]

RE: Question 1

Leave it in exact form.

[Collin Li]

It's in books but I've never seen VCAA make a question based on it (not sure if the study design specifies it).

[Collin Li]

Yes, they do. The 68% - 95% - 99.7% (empirical) rule I've seen in MM textbooks,

What do you mean by empirical? It's numerical, based from the formula the normal distribution is defined on. It's not evidence-based.

[excal]

I believe it's also referred to as the empirical rule.

[Collin Li]

What a strange name... haha

[/0]

Yes, they do. The 68% - 95% - 99.7% (empirical) rule I've seen in MM textbooks,

What do you mean by empirical? It's numerical, based from the formula the normal distribution is defined on. It's not evidence-based.

Isn't it true every time though? I mean, even for extreme cases of , it still gives those percentages.

[Mao]

remember that all normal distributions behave similarly. So yes, that rule still holds for extreme cases.

but also keep in mind that it is only an estimate, and it is only accurate to the number of significant figures it has... so for that above case, it might be accurate to ....