Suppose that follows a chi-square distribution with 20 degrees of freedom. Use the ALEKS calculator to answer the following. (a) Compute P(12≤x≤31). Round your answer to at least three decimal places. P(12 k) =0.1. Round your answer to at least two decimal places. k=

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Suppose that \( \chi^2 \) follows a chi-square distribution with 20 degrees of freedom. Use the ALEKS calculator to answer the following.

---

(a) Compute \( P(12 \leq \chi^2 \leq 31) \). Round your answer to at least three decimal places.

\[ P(12 \leq \chi^2 \leq 31) = \boxed{\ } \]

(b) Find \( k \) such that \( P(\chi^2 \geq k) = 0.1 \). Round your answer to at least two decimal places.

\[ k = \boxed{\ } \]
Transcribed Image Text:Suppose that \( \chi^2 \) follows a chi-square distribution with 20 degrees of freedom. Use the ALEKS calculator to answer the following. --- (a) Compute \( P(12 \leq \chi^2 \leq 31) \). Round your answer to at least three decimal places. \[ P(12 \leq \chi^2 \leq 31) = \boxed{\ } \] (b) Find \( k \) such that \( P(\chi^2 \geq k) = 0.1 \). Round your answer to at least two decimal places. \[ k = \boxed{\ } \]
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Degrees of freedom =20


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