The question is to find that value of x for which F(x)=0.3, where X follows Chi-square distribution with 13 df.
∫_0^x▒〖(e^((-x)/2) x^(n/2-1))/(2^(n/2) ⌈n/2┤ )=0.3〗
∫_0^x▒〖e^((-x)/2) x^(13/2-1 )=0.3* 2^(13/2)* ⌈13/2┤ 〗
I cannot move further. Can someone help?
Usually this is solved using the chi-squared tables
$$x\approx 9.93$$
Usually Paper Tables do not show $F(0.3)$. In a standard chi-square table you usually find $F(0.25)$ and $F(0.5)$ but with a simple gaussian approx you get
$$u_{0.3}=\frac{1}{2}\Bigg[z_{0.3}+\sqrt{2\times 13-1}\Bigg]^2=\frac{1}{2}\Big[-0.53+5\Big]^2\approx 9.99$$
Which is very close to the exact result of $9.93$ that I got with a calculator