[SparKeD]

X~N(15,4)

Find w to 2 d.p.

P(mod(X-15) < w ) = 0.9

Im confused. Any help pleeeaase

[astudent]

Expand the modulus bracket inside the probability.

[SparKeD]

I have, i get stuck @:

P(-(x-15)< w < (x-15) )

Next I modelled probability onto Z~N(0,1)

P(((-x-15)-15)/2) < Z < (((x-15)-15)/2) =0.9

P((x-30)/2)-P(-x/2) = 0.9
P((x-30)/2) + P( x/2) - 1 = 0.9

P( 1.2815 > w ) = 0.9

(x-30)/2 + x/2 - 1 = 1.2815

rearrage etc

x = 11.521

Plugged ths into P(mod(x-15) < w ) = 0.9

w = 3.479

The answer is 3.29

And im not entirely sure you can do half the steps i just used

[astudent]

Look at it this way, Let Y be a normal random variable such that, Y = X - 15, now Y~N(0,4)

And you want P(|y|<w); This means that the only area you are not looking for is 1-0.9 = 0.1; but since the normal is symmetric you have 0.05 of that on each side.

So now look up the Z value for a probability of 0.05 and plug it in to the standardization equation: Z = (w - 0)/2. This obtains the answer.

[TheNightmare]

I still do not understand.

Can anyone please go through this question:

If the random variable X is distributed as N(5,4), calculate:

P(modulus(X -5) > 3 ).


Thanks

[falcon pluse]

(Original post by TheNightmare)
I still do not understand.

Can anyone please go through this question:

If the random variable X is distributed as N(5,4), calculate:

P(modulus(X -5) > 3 ).


Thanks

l,

ok so this is the same as p (x-5>3)+p(x-5<-3)

so its basically p(x>8)+p(x<2)

Still want help with finding w?

[MathematicsKiller]

(Original post by TheNightmare)
I still do not understand.

Can anyone please go through this question:

If the random variable X is distributed as N(5,4), calculate:

P(modulus(X -5) > 3 ).


Thanks

This is basically:
P((x - 5) > 3) + P((x - 5) < -3)

= P(x > 8) + P(x < 2)

[TheNightmare]

(Original post by falcon pluse)
l,

ok so this is the same as p (x-5>3)+p(x-5<-3)

so its basically p(x>8)+p(x<2)

Still want help with finding w?

Thanks a lot. I think I got the hang of it now!

So the general rule is:

P(modulus(X-y) > q) = P(X-y > q ) + P(X-y < -q) right?

What if it was like this:

P(modulus(X-y) < q) would this be = P(X-y < q ) + P(X-y > -q) ?

[TheNightmare]

(Original post by MathematicsKiller)
This is basically:
P((x - 5) > 3) + P((x - 5) < -3)

= P(x > 8) + P(x < 2)

What is the answer?

According to my text book it is: 0.0668

but i'm somehow getting : 0.1336

What am I doing WRONG???

[MathematicsKiller]

(Original post by TheNightmare)
What is the answer?

According to my text book it is: 0.0668

but i'm somehow getting : 0.1336

What am I doing WRONG???

Are you sure you posted the question correctly?
I get the same answer as you.

I believe the answer in the text book is the answer you would get if there were no modulus.

[TheNightmare]

(Original post by MathematicsKiller)
Are you sure you posted the question correctly?
I get the same answer as you.

I believe the answer in the text book is the answer you would get if there were no modulus.

(Modulus is Bold and Underlined )

Yes the question is P( X-5 > 3).

So is the text book answer wrong?

[TheNightmare]

(Original post by falcon pluse)
l,

ok so this is the same as p (x-5>3)+p(x-5<-3)

so its basically p(x>8)+p(x<2)

Still want help with finding w?

What did you get as an answer?

According to my text book the answer is: 0.0668

but I am getting : 0.1336

Is the text book answer wrong?

[littleone271]

I miss statistics

[TheNightmare]

(Original post by littleone271)
I miss statistics

Will you be able this question for me:

If the random variable X is distributed as N(5,4), calculate:

P((X -5) > 3 ).

Modulus is in BOLD and is Underlined

Thanks

[littleone271]

(Original post by TheNightmare)
Will you be able this question for me:

If the random variable X is distributed as N(5,4), calculate:

P((X -5) > 3 ).

Modulus is in BOLD and is Underlined

Thanks

I used to be good at it and I did an AS in pure statistics but that was a couple of years ago and I havn't really done it properly since so I can't remember how to do it ... Sorry...

I remember this book being pretty amazing though because it's got worked examples and everything in it. I had this one for s1b and the s2 and s3 ones and they were all really good.

http://www.amazon.co.uk/Advancing-Ma...1519123&sr=1-1

[TheNightmare]

(Original post by littleone271)
I used to be good at it and I did an AS in pure statistics but that was a couple of years ago and I havn't really done it properly since so I can't remember how to do it ... Sorry...

I remember this book being pretty amazing though because it's got worked examples and everything in it. I had this one for s1b and the s2 and s3 ones and they were all really good.

http://www.amazon.co.uk/Advancing-Ma...1519123&sr=1-1

Ahh, I'm doing Statistics 1 with Edexcel not AQA. But never mind, thanks anyway.

[TheNightmare]

Can anyone answer this?

X~N(5,4) -------------------------------- Calculate: P( |X-5| > 3 ).