Question

Help please..What are the scores that separate the most extreme 5% of the population (from the middle 95%)? (5 points)..M=200,SD=50

Answer 1

What do you mean by M=200, SD=50?

Answer 2

\[\mu=200, \sigma=50\] @Ahsome

Answer 3

From the normal distribution, I hope you remember that when you standardize a normal random variable, then you have that \(P(-1.96\le Z \le 1.96)=0.95\), where \(Z\sim\mathrm{N}(0,1)\), i.e \(Z\) is the standard normal distribution. Recall that to standardize any normal distribution \(X\sim\mathrm{N}(\mu,\sigma^2)\) to get \(Z\), then you do \[ Z=\frac{X-\mu}{\sigma}\\ \, \\\implies X=\sigma Z+\mu\] So to find your critical values of \(X\), you substitute in the critical value for the standard normal in your equation:

\(X=50(-1.96) +200\)
and the other one is
\(X=50(1.96)+200 \)