Let Z1, Z2, ... Z7 be a random sample from the standard normal distribution N(0, 1). Let W = Z1 ^2, Z2 ^2, ... Z7 . Find P(1.69 < W < 14.07.

I have no idea where to begin with this one.

Thanks

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- Mar 1st 2011, 12:13 PMLaydieofsorrowsStandard Normal Distribution
Let Z1, Z2, ... Z7 be a random sample from the standard normal distribution N(0, 1). Let W = Z1 ^2, Z2 ^2, ... Z7 . Find P(1.69 < W < 14.07.

I have no idea where to begin with this one.

Thanks

- Mar 1st 2011, 05:01 PMmatheagle
I would guess that you mean W is the sum of the squares of the Z's which makes it a chi-square with 7 degress of freedom.

Otherwise W is a vector and you're missing 6 other parts of the question.

So go to a $\displaystyle \chi^2_7$ table and look up those numbers OR use....http://www.statsoft.com/textbook/dis...on-tables/#chi

from that the answer is .975-.05.