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# quick s3 question watch

1. Real quick question for anyone interested

why isn't the fourth line following the usual normal distribution layout of the random variable minus the mean all over the standard deviation? so it should be 0.5 - the mean?

so confused with what's going on in this question
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2. (Original post by Katiee224)
Real quick question for anyone interested

why isn't the fourth line following the usual normal distribution layout of the random variable minus the mean all over the standard deviation? so it should be 0.5 - the mean?

so confused with what's going on in this question
It's not quite what they're doing in this question.

Between lines 3 and 4, they've divided both sides by the standard deviation of the variable tbar. It transforms the left hand side inside the brackets into Z and the right hand side into a function of n and then you use that to find n.
3. (Original post by Katiee224)
Real quick question for anyone interested

why isn't the fourth line following the usual normal distribution layout of the random variable minus the mean all over the standard deviation? so it should be 0.5 - the mean?

so confused with what's going on in this question
We know that .

The way I like to do it is by finding a new distribution like this:

[ the mean, , has no variance]

and then we base our calculations off of the new distribution we found. Might even help to call it .

Zacken, how do you do these, out of interest?
4. (Original post by aymanzayedmannan)

Zacken, how do you do these, out of interest?
so we want

Hence, since

Which yields:

Standardising gives us

So we know that from the percentage points table.
5. (Original post by aymanzayedmannan)
We know that .

The way I like to do it is by finding a new distribution like this:

[ the mean, , has no variance]

and then we base our calculations off of the new distribution we found. Might even help to call it .

Zacken, how do you do these, out of interest?
I'm still a bit lost, how does this follow the rules of E(X-Y) = E(X) - E(Y) and Var(X-Y) = Var(X) + Var(Y)?

like how can you have E(x) with x being another mean? does that just equal 0?
6. (Original post by Katiee224)
I'm still a bit lost, how does this follow the rules of E(X-Y) = E(X) - E(Y) and Var(X-Y) = Var(X) + Var(Y)?

like how can you have E(x) with x being another mean? does that just equal 0?
using , but since then we have .

We also have so .
7. (Original post by Zacken)
using , but since then we have .

We also have so .
Okay so you are saying we treat as a constant?
8. (Original post by Katiee224)
Okay so you are saying we treat as a constant?
We treat it as a constant because it is a constant.
9. (Original post by Katiee224)
Okay so you are saying we treat as a constant?
The mean has no variance, so it is a constant.
10. okay i feel a bit stupid now haha, thanks for clearing that one up foe me guys
11. (Original post by Katiee224)
okay i feel a bit stupid now haha, thanks for clearing that one up foe me guys
Nothing to feel stupid about, it's good that you're asking these things.

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