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Learning about the Chi squared distribution - getting familiar with using the tables associated, and trying to understand the curve.

Problems such as

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Are as trivial as looking into the Chi-squared table!

Then I was presented with THIS, the final part of this problem (part c):

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And I am a tad stumped.

I know that the chi squared table typically gives $\mathrm{P}(X_a^2 < X^2)$. That is what made the first two problems a trivial table-look up. But what propertiesof Chi-Squared distribution can I employ to find the solution to the third part of this problem set?

Michael Hardy
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PinkElephantsOnParade
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1 Answers1

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If I can believe my software, if $X^2\sim\chi^2_{10}$, then $\Pr(X^2<23.21)=0.99$. Your table should confirm that.

Since $\Pr(X_a^2<X^2<23.21) = \Pr(X^2<23.21)-\Pr(X^2<X_a^2)$, you would need $$\Pr(X^2<X_a^2)=0.9975.\tag1$$ If your table gives you the value of $X_a^2$ for which $(1)$ is true, then you've got it.

Michael Hardy
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