You are Here: Home

# Stats - Normal Distribution-Modulus

Maths and statistics discussion, revision, exam and homework help.

Announcements Posted on
Find out how cards are replacing warnings on TSR...read more 03-12-2013
1. Stats - Normal Distribution-Modulus
X~N(15,4)

Find w to 2 d.p.

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

Im confused. Any help pleeeaase
2. Re: Stats - Normal Distribution-Modulus
Expand the modulus bracket inside the probability.
3. Re: Stats - Normal Distribution-Modulus
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

And im not entirely sure you can do half the steps i just used
4. Re: Stats - Normal Distribution-Modulus
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.
5. Re: Stats - Normal Distribution-Modulus
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
6. Re: Stats - Normal Distribution-Modulus
(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?
7. Re: Stats - Normal Distribution-Modulus
(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)
8. Re: Stats - Normal Distribution-Modulus
(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) ?
9. Re: Stats - Normal Distribution-Modulus
(Original post by MathematicsKiller)
This is basically:
P((x - 5) > 3) + P((x - 5) < -3)

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

According to my text book it is: 0.0668

but i'm somehow getting : 0.1336

What am I doing WRONG???
10. Re: Stats - Normal Distribution-Modulus
(Original post by TheNightmare)

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.
Last edited by MathematicsKiller; 12-03-2012 at 02:21.
11. Re: Stats - Normal Distribution-Modulus
(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?
Last edited by TheNightmare; 12-03-2012 at 02:38.
12. Re: Stats - Normal Distribution-Modulus
(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?
13. Re: Stats - Normal Distribution-Modulus
I miss statistics
14. Re: Stats - Normal Distribution-Modulus
(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
15. Re: Stats - Normal Distribution-Modulus
(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.

16. Re: Stats - Normal Distribution-Modulus
(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.

Ahh, I'm doing Statistics 1 with Edexcel not AQA. But never mind, thanks anyway.
17. Re: Stats - Normal Distribution-Modulus

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

## Step 2: Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank

this is what you'll be called on TSR

2. this can't be left blank

never shared and never spammed

3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. By completing the slider below you agree to The Student Room's terms & conditions and site rules

2. Slide the button to the right to create your account

You don't slide that way? No problem.

Last updated: March 15, 2012
Study resources