Chi square distribution questions and answers

Chi-square distribution

Find the median of the chi-square distribution with 22degrees of freedom. Round your answer to at least two decimal places

In the question above the resolution had the equation of P(Xsquare > M)=0.5. Where did the 0.5 come from? Is it coming from the previous question answer?

Chi-square distribution
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.

Additional Resources
Elementary Statistics (A Brief Version), 6th Ed.
Bluman
Chapter 7: Confidence Intervals and Sample Size
Section 7.4: Confidence Intervals for Variances and Standard Deviations

Supplementary Resources
We're asked to compute , where follows a chi-square distribution with degrees of freedom. Using the calculator, we can compute and use the complement rule to obtain :


.
(Note that, since the degrees of freedom in the above calculation must be specified for the ALEKS calculator, the expression appears as with in the calculator input.)

Figure 1

We are asked to find such that for a chi-square distribution with degrees of freedom. Note that such a is the value that cuts off an area of in the right tail of this distribution, that is, for the distribution. See Figure 1, which depicts the distribution and an area of shaded to the right of .
Using the calculator, we get

.
(Note that we have to use the input to specify the degrees of freedom.)

We're asked to find the median of the chi-square distribution with degrees of freedom. The median of a continuous distribution is the value that divides the distribution in half; in other words, the probability of obtaining a value greater than the median is and the probability of obtaining a value less than the median is .
In finding the median of the chi-square distribution with degrees of freedom, then, we are finding the value such that , where follows a chi-square distribution with degrees of freedom. In other words, we are finding . Using the calculator, we get

Comparing the mean and median of this distribution

.
The answer is:

Median

Chi-square distribution

Find the median of the chi-square distribution with 22degrees of freedom. Round your answer to at least two decimal places

In the question above the resolution had the equation of P(Xsquare > M)=0.5. Where did the 0.5 come from? Is it coming from the previous question answer?