Answer:
a) P(12≤χ²≤24)=0.690
b) k=35.85
c) Median=18.34
Step-by-step explanation:
The question is incomplete: "Use the calculator provided to solve the following problems. Suppose that χ² follows a chi-square distribution with 19 degrees of freedom. Compute P(12≤χ²≤24) . Round your answer to at least three decimal places.
Suppose again that χ² follows a chi-square distribution with 19 degrees of freedom. Find k such that P(χ²>k)=0.025. Round your answer to at least two decimal places.
Find the median of the chi-square distribution with 19 degrees of freedom. Round your answer to at least two decimal places."
Compute P(12≤χ²≤24)
[tex]P(12\leq\chi^2\leq24) =P(\chi^2\leq24)-P(\chi^2\leq12)\\\\P(12\leq\chi^2\leq24) =0.804-0.114\\\\P(12\leq\chi^2\leq24) =0.690[/tex]
Find k such that P(χ²>k)=0.025
[tex]k=35.85\\\\P(\chi^2>35.85)=0.025[/tex]
The median of the chi-square is:
[tex]M\approx k(1-\frac{2}{9k} )^3\\\\M\approx19(1-\frac{2}{9*19})^3\\\\M\approx 19*0.9883^3 =19*0.965=18.34[/tex]
