S1 normal distribution Watch

Byrney11
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Report Thread starter 7 years ago
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Basically i have attempted this question and have got it utterly wrong. when i looked at the mark scheme it was talking about using 0.8 as a figure instead of 0.6 due to symmetry. can anybody explain this and help me answer the question. Thanks

The random variable X~N(0,c^2)
Given that P(-4<X<4)=0.6 , find the value of 'c'
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Stormwhite
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Ok, due to symmetry, P(0&lt;X&lt;4) = 0.3, right? And P(X&lt;0)=0.5

Hence:
P(X&lt;4) = 0.8
Find the z value for P(Z&lt;z)=0.8 from tables.

Put that into the Standard distribution equation:
Z=\frac{X-\mu}{\sigma}

And there you have it.
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Byrney11
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i understand the 0.5 bit but where do you get 0.3 from ?
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Kareir
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(Original post by Byrney11)
i understand the 0.5 bit but where do you get 0.3 from ?
BEcause the curve is symetrical, so if you're told that the area between, say, -4 and 4 is 0.6, it's half and half on each side of 0. So 0.3 between 0 and 4, and 0.3 between -4 and 0, for a total of 0.6

_Kar.
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Byrney11
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thank you
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