Question

Use the calculator provided to solve the following problems. Suppose that follows a chi-square distribution with degrees of freedom. Compute . Round your answer to at least three decimal places. Suppose again that follows a chi-square distribution with degrees of freedom. Find such that . Round your answer to at least two decimal places. Find the median of the chi-square distribution with degrees of freedom. Round your answer to at least two decimal places.

Answer 1

a) P(12≤χ²≤24)=0.690

b) k=35.85

c) Median=18.34

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)

`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`

Find k such that P(χ²>k)=0.025

`k=35.85\\\\P(\chi^2>35.85)=0.025`

The median of the chi-square is:

`M\approx k(1-(2)/(9k) )^3\\\\M\approx19(1-(2)/(9*19))^3\\\\M\approx 19*0.9883^3 =19*0.965=18.34`