suppose that $chi^{2}$ follows a chi - square distribution with 24 degrees of freedom. use the aleks…

suppose that $chi^{2}$ follows a chi - square distribution with 24 degrees of freedom. use the aleks calculator to answer the following. (a) compute $p(13leqchi^{2}leq33)$. round your answer to at least three decimal places. $p(13leqchi^{2}leq33)=square$ (b) find $k$ such that $p(chi^{2}geq k)=0.05$. round your answer to at least two decimal places. $k = square$

suppose that $chi^{2}$ follows a chi - square distribution with 24 degrees of freedom. use the aleks calculator to answer the following. (a) compute $p(13leqchi^{2}leq33)$. round your answer to at least three decimal places. $p(13leqchi^{2}leq33)=square$ (b) find $k$ such that $p(chi^{2}geq k)=0.05$. round your answer to at least two decimal places. $k = square$

Answer

Explanation:

Step1: Recall chi - square distribution properties

We use the ALEKS calculator's chi - square distribution functions. For part (a), we find (P(13\leq\chi^{2}\leq33)) by calculating (P(\chi^{2}\leq33)-P(\chi^{2}\leq13)) with 24 degrees of freedom.

Step2: Calculate using ALEKS

Using the ALEKS calculator, for (\nu = 24), (P(\chi^{2}{24}\leq33)\approx0.879) and (P(\chi^{2}{24}\leq13)\approx0.059). Then (P(13\leq\chi^{2}\leq33)=0.879 - 0.059=0.820).

Step3: For part (b), use the right - tailed probability

We want to find (k) such that (P(\chi^{2}\geq k)=0.05) with 24 degrees of freedom. In the ALEKS calculator, we use the inverse - chi - square function for the right - tailed probability.

Step4: Find (k) value

Using the ALEKS calculator with (\nu = 24) and right - tailed probability (0.05), we get (k\approx36.415\approx36.42).

Answer:

(a) (0.820) (b) (36.42)