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 $p(chi^{2}leq17)$. round your answer to at least three decimal places. $p(chi^{2}leq17)=square$ (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 $p(chi^{2}leq17)$. round your answer to at least three decimal places. $p(chi^{2}leq17)=square$ (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: Use chi - square distribution table or calculator

We use a chi - square distribution calculator (since the problem mentions ALEKS calculator). For part (a), we input degrees of freedom $df = 24$ and the value $x = 17$ to find the cumulative probability $P(\chi^{2}\leq17)$.

Step2: For part (b)

We know that $P(\chi^{2}\geq k)=0.05$. This means $P(\chi^{2}<k)=1 - 0.05=0.95$. We input degrees of freedom $df = 24$ and cumulative probability $0.95$ into the chi - square distribution calculator to find the value of $k$.

Answer:

(a) Using a chi - square distribution calculator with $df = 24$ and $x = 17$, we get $P(\chi^{2}\leq17)\approx0.238$. (b) Using a chi - square distribution calculator with $df = 24$ and cumulative probability $0.95$, we get $k\approx36.42$.