Question

When does the chi-square curve approximate a normal distribution?

Short answer

If $df>90$because chi square is approximated as a normal curve, this suggests that the distribution is normal.

$X~N\left(1000,44.72\right)$

Step-by-step solution

Given Information

We have to determine when does the chi-square curve approximate a normal distribution.

Explanation

Formulas using here is as follows

${\mu }_{x^2}=df$

${\sigma }_{x^2}=\sqrt{2\times df}$

If $df>90$because chi square is approximated as a normal curve, this suggests that the distribution is normal.

for $X~{X^2}_{1000}$the population mean will be

$$\begin{gathered} \mu =df \\ df=1000 \\ \mu =1000 \end{gathered}$$

standard deviation will be

$$\begin{gathered} \sigma =\sqrt{2\times df} \\ =\sqrt{2\times 1000} \\ \approx 44.72 \end{gathered}$$

Therefore we have

$X~N\left(1000,44.72\right)approx$