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Old 4th September 2012, 02:30 PM   #1 (permalink)
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Need help with H2 Maths Statistics - Normal Distribution (invNorm)

This is the question:

Given that W~N(6,6), find the value of a for the following:

P(|W| < a) = 0.01

The correct answer is a=0.588

What's wrong with my working?

LHS:
P(|W| < a)
= P(-a < W < a)
= P(W<a) - P(W<-a)
= P(W<a) - P(W>a)
= P(W<a) - [1-P(W<a)]
= 2P(W<a) - 1

Hence:
2P(W<a) - 1 = 0.01
P(W<a) = 1.01/2
P(W<a) = 0.505

Using GC:
invNorm (0.505, 6, √6) = 6.03

a = 6.03

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Last edited by Budfred; 4th September 2012 at 02:35 PM.
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Old 4th September 2012, 04:08 PM   #2 (permalink)
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Re: Need help with H2 Maths Statistics - Normal Distribution (invNorm)

Originally Posted by Budfred View Post
This is the question:

Given that W~N(6,6), find the value of a for the following:

P(|W| < a) = 0.01

The correct answer is a=0.588

What's wrong with my working?

LHS:
P(|W| < a)
= P(-a < W < a)
= P(W<a) - P(W<-a)
= P(W<a) - P(W>a)
= P(W<a) - [1-P(W<a)]
= 2P(W<a) - 1

Hence:
2P(W<a) - 1 = 0.01
P(W<a) = 1.01/2
P(W<a) = 0.505

Using GC:
invNorm (0.505, 6, √6) = 6.03

a = 6.03
The bold underlined statement is wrong, as W is not a standard normal distribution.

My working:

P(-a<w<a) = 0.01

Using GC:
Y1=normalcdf(-x,x,6,6^0.5)
Y2=0.01

Find interception point to find x, which is the value for a.

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Last edited by Tetrahedron; 4th September 2012 at 04:09 PM.
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Old 4th September 2012, 05:22 PM   #3 (permalink)
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Re: Need help with H2 Maths Statistics - Normal Distribution (invNorm)

Thanks got it!


Last edited by Budfred; 4th September 2012 at 05:29 PM.
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Old 4th September 2012, 11:19 PM   #4 (permalink)
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Re: Need help with H2 Maths Statistics - Normal Distribution (invNorm)

To add on:
Just pressing into GC without modifying the window will not get any answer.

Remember to set
y min 0
y max 0.05

(Since your second equation is y = 0.01, you do not want min -10/max 10 because you will see nothing)

x min -1
x max 1

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Last edited by .Memo; 4th September 2012 at 11:26 PM.
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