Question

If $df>90$, the distribution is _____________. If$df=15,$ the distribution is _______________

Short answer

Because the chi-square curve is approximated as a normal curve if $df>90$, the distribution is Normal.

$X~N(1000,44.72)$

Because the chi-square curve bends towards the right side of the curve when $df=15$, the distribution is right skewed.

Step-by-step solution

Given information

Given in the question that, We need to find the distribution if $df>90$and , the $df=15$.

Explanation

Because the chi-square curve is approximated as a normal curve if $df>90$, the distribution is Normal.

The population mean for $X~{\chi }_{1000}^2$ is determined as follows:

$\mu =df$

$=1000$

$\Rightarrow \mu =1000$

Also known as standard deviation, it is determined as follows:

$\sigma =\sqrt{2\times df}$

$$\begin{gathered} =\sqrt{2\times 1000} \\ =\sqrt{2000} \\ =44.721 \\ \approx 44.72 \end{gathered}$$

$\Rightarrow \sigma =44.72$

Consequently, we have

$X~N(1000,44.72)$approx.

Because the chi-square curve bends towards the right side of the curve when $df=15$, the distribution is right skewed.