Suppose that x follows a chi-square distribution with 21 degrees of freedom. Compute P(11

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### Chi-Square Distribution Problems – Educational Guide

This section covers problems related to the chi-square distribution and student exercises for mastering these concepts.

1. **Suppose that \( \chi^2 \) follows a chi-square distribution with 21 degrees of freedom. Compute \( P(11 \leq \chi^2 \leq 27) \). Round your answer to at least three decimal places.**

2. **Suppose again that \( \chi^2 \) follows a chi-square distribution with 21 degrees of freedom. Find \( k \) such that \( P(\chi^2 \geq k) = 0.025 \). Round your answer to at least two decimal places.**

3. **Find the median of the chi-square distribution with 21 degrees of freedom. Round your answer to at least two decimal places.**
    - Median \( = \) 
    
    ![Graphical Elements]
    - There is a box with three input fields labeled for entering values:
        - \( k = \)
        - (Calculation related to \( \chi^2 \) parameters)
        - Median \( = \)

These exercises require students to use statistical tables or software tools (like R, Python, or statistical calculators) to find the probabilities and median values for the chi-square distribution with specified degrees of freedom. 

Students should ensure their answers are rounded to the required number of decimal places for accuracy.

### Visual Aid Description

- The provided graphical box shows spaces for entering computed values of \( k \) and the median of the chi-square distribution.
Transcribed Image Text:### Chi-Square Distribution Problems – Educational Guide This section covers problems related to the chi-square distribution and student exercises for mastering these concepts. 1. **Suppose that \( \chi^2 \) follows a chi-square distribution with 21 degrees of freedom. Compute \( P(11 \leq \chi^2 \leq 27) \). Round your answer to at least three decimal places.** 2. **Suppose again that \( \chi^2 \) follows a chi-square distribution with 21 degrees of freedom. Find \( k \) such that \( P(\chi^2 \geq k) = 0.025 \). Round your answer to at least two decimal places.** 3. **Find the median of the chi-square distribution with 21 degrees of freedom. Round your answer to at least two decimal places.** - Median \( = \) ![Graphical Elements] - There is a box with three input fields labeled for entering values: - \( k = \) - (Calculation related to \( \chi^2 \) parameters) - Median \( = \) These exercises require students to use statistical tables or software tools (like R, Python, or statistical calculators) to find the probabilities and median values for the chi-square distribution with specified degrees of freedom. Students should ensure their answers are rounded to the required number of decimal places for accuracy. ### Visual Aid Description - The provided graphical box shows spaces for entering computed values of \( k \) and the median of the chi-square distribution.
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